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SATOH Shin
Graduate School of Science / Division of Mathematics
Professor

Researcher basic information

■ Research Keyword
  • 2-knot theory
■ Research Areas
  • Natural sciences / Geometry

Research activity information

■ Paper
  • Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh, Kodai Wada
    Hiroshima University - Department of Mathematics, Jul. 2025, Hiroshima Mathematical Journal, 55(2) (2)
    Scientific journal

  • Ryuji Higa, Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh
    In the previous papers, we introduced three intersection polynomials of a virtual knot. In this paper, we prove that the first and second intersection polynomials are finite-type invariants of order two with respect to crossing change. We also study virtual knots of supporting genus one, and give a relation between the first and second intersection polynomials of such a virtual knot.
    World Scientific Pub Co Pte Ltd, Feb. 2025, Journal of Knot Theory and Its Ramifications, 34(04) (04)
    Scientific journal

  • Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh, Kodai Wada
    We introduce a local deformation called the virtualized [Formula: see text]-move for virtual knots and links. We prove that the virtualized [Formula: see text]-move is an unknotting operation for virtual knots. Furthermore we give a necessary and sufficient condition for two virtual links to be related by a finite sequence of virtualized [Formula: see text]-moves.
    World Scientific Pub Co Pte Ltd, Oct. 2024, Journal of Topology and Analysis, 18(02) (02), 409 - 421
    Scientific journal

  • Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh, Kodai Wada
    Oct. 2024, arXiv preprint, English

  • Jean-Baptiste Meilhan, Shin Satoh, Kodai Wada
    Institute of Mathematics, Polish Academy of Sciences, 2023, Fundamenta Mathematicae, 263(3) (3), 203 - 234
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Writhe polynomials and shell moves for virtual knots and links
    T. Nakamura, Y. Nakanishi, S. Satoh
    2020, European J. Combin., 84, 103033 - 24 pp, English
    [Refereed]
    Scientific journal

  • A note on coverings of virtual knots
    T. Nakamura, Y. Nakanishi, S. Satoh
    2020, J. Knot Theory Ramifications, 29(8) (8), 1971002 - 11 pp, English
    [Refereed]
    Scientific journal

  • The pass move is an unknotting operation for welded knots
    T. Nakamura, Y. Nakanishi, S. Satoh, A. Yasuhara
    Sep. 2018, Topology Appl., 247, 9 - 19, English
    [Refereed]
    Scientific journal

  • Finiteness of the set of virtual knots with a given state number
    T. Nakamura, Y. Nakanishi, S. Satoh
    2018, J. Knot Theory Ramifications, 27(no. 8) (no. 8), 1850049 - 16 pp, English
    [Refereed]
    Scientific journal

  • Crossing changes, delta moves and sharp moves on welded knots
    S. Satoh
    2018, Rocky Mountain J. Math., 48(3) (3), 967 - 979, English
    [Refereed]
    Scientific journal

  • T. Hayashi, T. Nakamura, Y. Nakanishi, S. Satoh
    Sep. 2017, J. Knot Theory Ramifications, 26(10) (10), 1750060 - 9 pp, English
    [Refereed]
    Scientific journal

  • T. Nakamura, Y. Nakanishi, M. Saito, S. Satoh
    Jul. 2017, J. Knot Theory Ramifications, 26(8) (8), 1750047 - 6 pp, English
    [Refereed]
    Scientific journal

  • The 6- and 8-palette numbers of links
    T. Nakamura, Y. Nakanishi, M. Saito, S. Satoh
    Apr. 2017, Topology Appl., 222, 200 - 216, English
    [Refereed]
    Scientific journal

  • Y. Funahashi, Y. Nakanishi, S. Satoh
    Nov. 2016, J. Knot Theory Ramifications, 25(13) (13), 1671001 - 4 pp, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • T. Nakamura, Y. Nakanishi, S. Satoh
    Apr. 2016, J. Knot Theory Ramifications, 25(4) (4), 1650017 - 22 pp, English
    [Refereed]
    Scientific journal

  • S. Satoh
    2016, Algebr. Geom. Topol., 16(6) (6), 3325 - 3359, English
    [Refereed]
    Scientific journal

  • Y. Nakanishi, S. Satoh
    Dec. 2015, Topology Appl., 196(B) (B), 846 - 851, English
    [Refereed]
    Scientific journal

  • T. Nakamura, Y. Nakanishi, S. Satoh
    Dec. 2015, Topology Appl., 196(B) (B), 754 - 770, English
    [Refereed]
    Scientific journal

  • Y. Nakanishi, Y. Sakamoto, S. Satoh
    Dec. 2015, Topology Appl., 196(B) (B), 771 - 776, English
    [Refereed]
    Scientific journal

  • T. Nakamura, Y. Nakanishi, S. Satoh
    Oct. 2014, J. Knot Theory Ramifications, 23(12) (12), 1450059 - 15 pp, English
    [Refereed]
    Scientific journal

  • T. Nakamura, Y. Nakanishi, S. Satoh, Y. Tomiyama
    Mar. 2014, J. Knot Theory Ramifications, 23(3) (3), 1450016 - 27 pp, English
    [Refereed]
    Scientific journal

  • 7-colored 2-knot diagram with six colors
    K. Oshiro, S. Satoh
    Mar. 2014, Hiroshima Math. J., 44(1) (1), 63 - 74, English
    [Refereed]
    Scientific journal

  • S. Satoh, K. Taniguchi
    2014, Fund. Math., 225(1) (1), 327 - 342, English
    [Refereed]
    Scientific journal

  • The pallet graph of a Fox coloring
    T. Nakamura, Y. Nakanishi, S. Satoh
    Yokohama City Unicersity and Yokohama National University, 2013, Yokohama Math. J., 59, 91 - 97, English
    [Refereed]
    Scientific journal

  • R. Higa, Y. Nakanishi, S. Satoh, T. Yamamoto
    Oct. 2012, J. Knot Theory Ramifications, 21(12) (12), 1250117 - 11 pp, English
    [Refereed]
    Scientific journal

  • T. Nakamura, Y.a Nakanishi, S. Satoh, Y. Tomiyama
    Sep. 2012, J. Knot Theory Ramifications, 21(10) (10), 1250095 - 18 pp, English
    [Refereed]
    Scientific journal

  • On the crossing numbers of a virtual knot
    S. Satoh, Y. Tomiyama
    Jan. 2012, Proc. Amer. Math. Soc., 140(1) (1), 367 - 376, English
    [Refereed]
    Scientific journal

  • A note on the sheet numbers of twist-spun knots
    S. Satoh
    Mar. 2010, Hiroshima Math. J., 40(1) (1), 1 - 15, English
    [Refereed]
    Scientific journal

  • 5-colored knot diagram with four colors
    S. Satoh
    Dec. 2009, Osaka J. Math., 46(4) (4), 939 - 948, English
    [Refereed]
    Scientific journal

  • S. Satoh
    Sep. 2009, Kyushu J. Math., 63(2) (2), 239 - 252, English
    [Refereed]
    Scientific journal

  • S. Satoh
    Apr. 2009, J. Math. Soc. Japan, 61(2) (2), 579 - 606, English
    [Refereed]
    Scientific journal

  • A note on the shadow cocycle invariant of a knot with a base point
    S. Satoh
    Sep. 2007, J. Knot Theory Ramifications, 16(7) (7), 959 - 967, English
    [Refereed]
    Scientific journal

  • Sheet numbers and cocycle invariants of surface-knots
    S. Satoh
    2007, Intelligence of low dimensional topology 2006, Ser. Knots Everything, 40, 287 - 291, English
    [Refereed][Invited]
    International conference proceedings

  • J. S. Carter, M. Elhamdadi, M. Saito, S. Satoh
    Sep. 2006, Topology Appl., 153(15) (15), 2788 - 2794, English
    [Refereed]
    Scientific journal

  • Ribbon concordance of surface-knots via quandle cocycle invariants
    J. S. Carter, M. Saito, S. Satoh
    Feb. 2006, J. Aust. Math. Soc., 80(1) (1), 131 - 147, English
    [Refereed]
    Scientific journal

  • Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers
    J. S. Carter, M. Saito, S. Satoh
    2006, Proc. Amer. Math. Soc., 134(9) (9), 2779 - 2783, English
    [Refereed]
    Scientific journal

  • The Braid index is not additive for the connected sum of 2-knots
    S. Kamada, S. Satoh, M. Takabayashi
    2006, Trans. Amer. Math. Soc., 358(12) (12), 5425 - 5439, English
    [Refereed]
    Scientific journal

  • M. Saito, S. Satoh
    Nov. 2005, J. Knot Theory Ramifications, 14(7) (7), 853 - 858, English
    [Refereed]
    Scientific journal

  • Non-additivity for triple point numbers on the connected sum of surface-knots
    S. Satoh
    2005, Proc. Amer. Math. Soc., 133(2) (2), 613 - 616, English
    [Refereed]
    Scientific journal

  • An infinite family of non-invertible surfaces in 4-space
    S. Asami, S. Satoh
    2005, Bull. London Math. Soc., 37(2) (2), 285 - 296, English
    [Refereed]
    Scientific journal

  • Triple point numbers and quandle cocycle invariants of knotted surfaces in 4-space
    S. Satoh, A. Shima
    2005, New Zealand J. Math., 34(1) (1), 71 - 79, English
    [Refereed]
    Scientific journal

  • Liftability for double coverings of immersions of non-orientable surfaces into 3-space
    K. Ichihara, S. Satoh
    2005, Houston J. Math, 31(3) (3), 721 - 741, English
    [Refereed]
    Scientific journal

  • No 2-knot has triple point number two or three
    S. Satoh
    2005, Osaka J. Math., 42(3) (3), 543 - 556, English
    [Refereed]
    Scientific journal

  • The 2-twist-spun trefoil has the triple point number four
    S. Satoh, A. Shima
    2004, Trans. Amer. Math. Soc., 356(3) (3), 1007 - 1024, English
    [Refereed]
    Scientific journal

  • A note on non-classical virtual knots
    T. Kishino, S. Satoh
    2004, J. Knot Theory Ramifications, 13(7) (7), 845 - 856, English
    [Refereed]
    Scientific journal

  • A note on unknotting numbers of twist-spun knots
    S. Satoh
    Kobe University, 2004, Kobe J. Math., 21(1-2) (1-2), 71 - 82, English
    [Refereed]
    Scientific journal

  • Tangles with up to seven crossings
    T. Kanenobu, H. Saito, S. Satoh
    2003, Proceedings of the Winter Workshop of Topology/Workshop of Topology and Computer, Interdiscip. Inform. Sci., 9(1) (1), 127 - 140, English
    [Refereed][Invited]
    International conference proceedings

  • Triple point invariants of non-orientable surface-links
    S. Satoh
    2002, Proceedings of the First Joint Japan-Mexico Meeting in Topology (Morelia, 1999), Topology Appl., 121(1-2) (1-2), 207 - 218, English
    [Refereed]
    International conference proceedings

  • Surface diagrams of twist-spun 2-knots
    S. Satoh
    2002, Knots 2000 Korea, Vol. 1 (Yongpyong), J. Knot Theory Ramifications, 11(3) (3), 413 - 430, English
    [Refereed]
    International conference proceedings

  • Bordism of undirected surfaces in 4-space
    J. S. Carter, S. Kamada, M. Saito, S. Satoh
    2002, Michigan Math. J., 50(3) (3), 575 - 591, English
    [Refereed]
    Scientific journal

  • A virtualized skein relation for Jones polynomials
    N. Kamada, S. Nakabo, S. Satoh
    2002, Illinois J. Math., 46(2) (2), 467 - 475, English
    [Refereed]
    Scientific journal

  • Congruence formulae for stable maps of surfaces
    S. Satoh
    Hiroshima University, 2002, Hiroshima Math. J., 32(3) (3), 351 - 369, English
    [Refereed]
    Scientific journal

  • Positive, alternating, and pseudo-ribbon surface-knots
    S. Satoh
    Kobe University, 2002, Kobe J. Math., 19(1-2) (1-2), 51 - 59, English
    [Refereed]
    Scientific journal

  • Minimal triple point numbers of some non-orientable surface-links
    S. Satoh
    2001, Pacific J. Math., 197(1) (1), 213 - 221, English
    [Refereed]
    Scientific journal

  • A theorem of Sanderson on link bordisms in dimension 4
    J. S. Carter, S. Kamada, M. Saito, S. Satoh
    2001, Algebr. Geom Topol., 1, 299 - 310, English
    [Refereed]
    Scientific journal

  • Double decker sets of generic surfaces in 3-space as homology classes
    S. Satoh
    2001, Illinois J. Math., 45(3) (3), 823 - 832, English
    [Refereed]
    Scientific journal

  • On non-orientable surfaces in 4-space which are projected with at most one triple point
    S. Satoh
    2000, Proc. Amer. Math. Soc., 128(9) (9), 2789 - 2793, English
    [Refereed]
    Scientific journal

  • Simplex moves on elementary surfaces
    S. Satoh
    Osaka University and Osaka City University, Departments of Mathematics, 2000, Osaka J. Math., 37(1) (1), 73 - 92, English
    [Refereed]
    Scientific journal

  • Virtual knot presentation of ribbon torus-knots
    S. Satoh
    2000, J. Knot Theory Ramifications, 9(4) (4), 531 - 542, English
    [Refereed]
    Scientific journal

  • Lifting a generic surface in 3-space to an embedded surface in 4-space
    S. Satoh
    2000, Topology Appl., 106(1) (1), 103 - 113, English
    [Refereed]
    Scientific journal

  • Sphere-slice links with at most five components
    S. Satoh
    1998, J. Knot Theory Ramifications, 7(2) (2), 217 - 230, English
    [Refereed]
    Scientific journal

■ Lectures, oral presentations, etc.
  • No 2-knot has regular triple point number four
    Shin SATOH
    Friday Seminar on Knot Theory, Nov. 2018, English, 大阪市立大学, International conference
    [Invited]
    Invited oral presentation

  • The n-cable of a ribbon 2-knot
    Shin SATOH
    Four dimensional Topology, Sep. 2018, English, 大阪市立大学, International conference
    [Invited]
    Invited oral presentation

  • Double point circles of regular 2-knot diagrams
    Shin SATOH
    拡大KOOK セミナー2018, Sep. 2018, Japanese, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • 2 次元結び目の多重化について
    Shin SATOH
    2017 年度琉球結び目セミナー, Jan. 2018, Japanese, 那覇市ぶんかテンブス館, Domestic conference
    [Invited]
    Invited oral presentation

  • リボン曲面タングルと曲面絡み目のダブル
    Shin SATOH
    2017 年度秋季総合分科会, Sep. 2017, Japanese, 山形大学, Domestic conference
    Oral presentation

  • A set of local moves generating the writhe polynomial
    Yasutaka NAKANISHI, Shin SATOH
    日本数学会・トポロジー分科会, Sep. 2017, Japanese, 山形大学理学部, Domestic conference
    Oral presentation

  • A set of local moves generating the writhe polynomial
    Shin SATOH
    拡大KOOKセミナー2017, Aug. 2017, Japanese, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • 単純 2 次元結び目図式の OU グラフについて
    SATO Shin
    2016年度琉球結び目セミナー, Dec. 2016, Japanese, 那覇市伝統工芸館, Domestic conference
    [Invited]
    Invited oral presentation

  • The ribbon stable class of a surface-link
    SATO Shin
    Friday Seminar on Knot Theory, Dec. 2016, English, Osaka City Uvinersity, Domestic conference
    [Invited]
    Invited oral presentation

  • Fundamental deformations on unwrithed surface-kntos
    SATO Shin
    4次元トポロジー, Nov. 2016, Japanese, Osaka City Uvinersity, Domestic conference
    [Invited]
    Invited oral presentation

  • A construction of stable classes of ribon surface-knots from non-ribbon surface-knots
    SATO Shin
    KOOK-TAPU Workshop of Knots in Tsushima Island, Sep. 2016, English, 対馬市交流センター, International conference
    [Invited]
    Invited oral presentation

  • 曲面結び目のねじれのない射影図
    SATO Shin
    拡大 KOOK セミナー, Aug. 2016, Japanese, Osaka Electro-Communication University, Domestic conference
    [Invited]
    Invited oral presentation

  • Weaving a fabric in 4-space
    SATO Shin
    拡大KOOKセミナー, Aug. 2016, Japanese, 神戸大学百年記念館, Domestic conference
    [Invited]
    Invited oral presentation

  • 曲面結び目の射影図の正則変形
    SATO Shin
    2016琉球結び目セミナー, Feb. 2016, Japanese, 那覇市ぶんかテンブス館, Domestic conference
    [Invited]
    Invited oral presentation

  • Dehn colored knot diagrams
    SATO Shin
    The 11th East Asian School of Knots and Related Topics, Jan. 2016, English, 大阪市立大学, International conference
    [Invited]
    Invited oral presentation

  • Noded knots and ribbon Kb-knots
    SATO Shin
    Friday Seminar on Knot Theory, Oct. 2015, Japanese, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Description of a surface-knot
    SATO Shin
    トポロジーとコンピュータ2014, Nov. 2014, English, 東京大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Local moves on welded knots
    SATO Shin
    東北結び目セミナー2014, Oct. 2014, Japanese, カレッジプラザ秋田, Domestic conference
    [Invited]
    Invited oral presentation

  • 交差交換で溶接結び目をほどく
    SATO Shin
    日本数学会秋季総合分科会, Sep. 2014, Japanese, 広島大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Delta-crossing number for knots
    NAKANISHI Yasutaka, SAKAMOTO Youko, SATO Shin
    日本数学会・トポロジー分科会, Sep. 2014, Japanese, 広島大学, Domestic conference
    Oral presentation

  • Crossing changes unknot a welded knot
    SATO Shin
    A Satellite Conference of Seoul ICM 2014 No. 25: Knots and Low Dimensional Manifolds, Aug. 2014, English, BEXCO, Busan, Korea, International conference
    [Invited]
    Invited oral presentation

  • 結び目のステイト数
    SATO Shin
    写像の特異点論及び関連する科学の諸問題, Jun. 2014, Japanese, 都城工業高等専門学校, Domestic conference
    [Invited]
    Invited oral presentation

  • 2次元結び目のザイフェルト超曲面
    SATO Shin
    2014琉球結び目セミナー, Jun. 2014, Japanese, 那覇ぶんかテンブス館, Domestic conference
    [Invited]
    Invited oral presentation

  • Effective 9-colorings for knots
    SATO shin
    Knots in Washington XXXVII, Jan. 2014, English, George WashingtonUniversity, Washington(米国), International conference
    [Invited]
    Invited oral presentation

  • 本質的フォックス彩色について
    SATO shin
    2013琉球結び目セミナー, Sep. 2013, Japanese, 那覇ぶんかテンブス館, Domestic conference
    [Invited]
    Invited oral presentation

  • Surface-tangle decomposition of ribbon 2-knots and twist-spun knots
    SATO shin
    International Conferenceon Topology and Geometry 2013 - JAMEX VI, Sep. 2013, English, 島根大学, 島根, International conference
    [Invited]
    Invited oral presentation

  • Delta-crossing number for knots
    NAKANISHI yasutaka, Yoko Sakamoto, SATO shin
    International Conference on Topology and Geometry 2013, Joint with the 6th Japan-Mexico Topology Symposium, Sep. 2013, English, 島根大学, 島根, International conference
    [Invited]
    Invited oral presentation

  • On knots with no 3-state
    SATO shin
    Friday Seminar on Knot Theory, Jun. 2013, English, 大阪市立大学, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • 結び目のOU列とその応用
    SATOH SHIN
    日本数学会2013年度年会, Mar. 2013, Japanese, 京都大学, Domestic conference
    Oral presentation

  • The pallet graph of a Fox coloring
    SATOH Shin
    Knots in Washington XXXV, Dec. 2012, English, George Washington University, International conference
    Oral presentation

  • The pallet graph of a Fox coloring
    SATOH SHIN
    東北結び目セミナー2012, Oct. 2012, Japanese, 山形大学小白川キャンパス, Domestic conference
    Oral presentation

  • 平面曲線と結び目のステイト数
    SATOH SHIN
    日本数学会2012年度秋季総合分科会, Sep. 2012, Japanese, 九州大学, Domestic conference
    Oral presentation

  • ある行列式の計算とその応用
    SATOH Shin
    2012琉球結び目セミナー, Sep. 2012, Japanese, 那覇市ぶんかテンブス館, Domestic conference
    Oral presentation

  • Crossing information and warping polynomials about the trefoil knot
    NAKANISHI Yasutaka, SATOH Shin, Takuto Yamamoto, Ryuji Higa
    2012 TAPU Workshop on Knot Theory and Related Topics2012 TAPU Summer School on Quandle Theory(The 4th TAPU-KOOK Joint Seminar on Knot Theory and Related Topicsand The 6th Graduate Student Workshop on Mathematics), Jul. 2012, English, Pusan National University, International conference
    [Invited]
    Invited oral presentation

  • Virtual graph presentations of ribbon surface-knots
    SATOH Shin
    The 8th East Asian School of Knots and Related Topics, Jan. 2012, English, 河内 明夫, KAIST, Daejeon, Korea, International conference
    [Invited]
    Invited oral presentation

  • Non-identical twin groups of virtual knot
    SATOH Shin
    Quantum Topology/Hopf Algebra Seminar, Oct. 2011, English, L. H. Kauffman, Illinois University at Chicago, International conference
    [Invited]
    Invited oral presentation

  • Quandle cocycle invariants of roll-spun knots
    SATOH Shin
    Virtual Seminar, Sep. 2011, English, D. Roseman, Iowa University, International conference
    [Invited]
    Invited oral presentation

  • Quandle cocycle invariants of roll-spun knots
    SATOH Shin
    Intelligence of Low-dimensional Topology, May 2011, Japanese, 大槻 知忠, 京都大学数理解析研究所, Domestic conference
    [Invited]
    Invited oral presentation

  • ロールスパン結び目のカンドル不変量
    SATOH Shin
    日本数学会年会, Mar. 2011, Japanese, 日本数学会, 早稲田大学, Domestic conference
    Oral presentation

  • Fox colorings and cocycle invariants of roll-spun knots
    SATOH Shin
    Mathematics Colloquium, Sep. 2010, English, M. Saito, University of South Florida, U.S.A., International conference
    [Invited]
    Invited oral presentation

  • Fox colorings and cocycle invariants of roll-spun knots
    SATOH Shin
    Knots in Chicago, Sep. 2010, English, L. H. Kauffman, University of Illinois at Chicago, U.S.A., International conference
    Oral presentation

  • Application of length of quandle 3-cocycle to surface-knot theory
    SATOH Shin
    The sixth East Asian School of Knots and Related topics, Jan. 2010, English, 河内 明夫, Nankai University, China, International conference
    [Invited]
    Invited oral presentation

  • 5次二面体カンドルの3コサイクルの長さ
    SATOH Shin
    日本数学会秋季総合分科会, Sep. 2009, Japanese, 日本数学会, 大阪大学, Domestic conference
    Oral presentation

  • The triple point number of the 2-twist-spun figure-eight knot
    SATOH Shin
    The first KOOK-TAPU Joint Seminar on Knot Theory and Related Topics, Aug. 2009, English, 河内 明夫, Osaka City University, International conference
    [Invited]
    Invited oral presentation

  • 5次二面体カンドルの望月コサイクルの長さとその応用
    SATOH Shin
    Workshop on Topology and Geometry, Jul. 2009, Japanese, 鎌田 聖一, 広島大学, Domestic conference
    Oral presentation

  • 非自明$2$次元結び目のシート数は$4$以上
    SATOH Shin
    日本数学会年会, Mar. 2009, Japanese, 日本数学会, 東京大学, Domestic conference
    Oral presentation

  • 曲面結び目の射影図について
    SATOH Shin
    第6回城崎新人セミナー, Feb. 2009, Japanese, 森 伸吾, 兵庫県豊岡市城崎町, Domestic conference
    [Invited]
    Invited oral presentation

  • Every non-trivial 2-knot needs four sheets
    SATOH Shin
    研究集会「4次元トポロジー」, Jan. 2009, Japanese, 鎌田 聖一, 広島大学, Domestic conference
    Oral presentation

  • Every non-trivial 2-knot needs four sheets
    SATOH Shin
    GThe 5th East Asian School of Knots and Related Topics, Jan. 2009, English, 河内 明夫, 慶州・韓国, International conference
    Oral presentation

  • Triviality of 2-knot with three sheets
    SATOH Shin
    研究集会「結び目の数学」, Dec. 2008, Japanese, 大山 淑之, 東京女子大学, Domestic conference
    Oral presentation

  • 結び目を5彩色するときに必要な色の数
    SATOH Shin
    北陸結び目セミナー「不変量と局所変形」, Nov. 2008, Japanese, 新國 亮, 金沢大学, Domestic conference
    Oral presentation

  • Triviality of 2-knot with three sheets
    SATOH Shin
    Friday seminar on Knot Theory, Nov. 2008, Japanese, 河内 明夫, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Triviality of 2-knot with one or two sheets
    SATOH Shin
    Intelligence of Low Dimensional Topology 兼拡大KOOKセミナー, Oct. 2008, Japanese, 河内 明夫, 大阪市立大学, Domestic conference
    Oral presentation

  • 5彩色可能な結び目の4色で塗られる射影図
    SATOH Shin
    日本数学会秋季総合分科会, トポロジー分科会, Sep. 2008, Japanese, 日本数学会, 東京工業大学, Domestic conference
    Oral presentation

  • 結び目の表示2
    SATOH Shin
    夏の学校「低次元トポロジーにおける未解決問題」, Aug. 2008, Japanese, 川村 友美, 名古屋大学, Domestic conference
    [Invited]
    Invited oral presentation

  • カンドルホモロジーと結び目不変量
    SATOH Shin
    夏の学校「低次元トポロジーにおける未解決問題」, Aug. 2008, Japanese, 川村 友美, 名古屋大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Triviality of 2-knot with one or two sheets
    SATOH Shin
    トポロジー・幾何セミナー, Jul. 2008, Japanese, 鎌田 聖一, 広島大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Triviality of 2-knot with one or two sheets
    SATOH Shin
    幾何学的視点からの特異点論, Jun. 2008, Japanese, 佐伯 修, 九州大学, Domestic conference
    Oral presentation

  • シート数1の2次元結び目の自明性
    SATOH Shin
    トポロジー金曜セミナー, May 2008, Japanese, 佐伯 修, 九州大学, Domestic conference
    [Invited]
    Invited oral presentation

  • 三重点数4の3彩色可能な2次元結び目について
    SATOH Shin
    日本数学会トポロジー分科会, Mar. 2008, Japanese, 日本数学会, 近畿大学, Domestic conference
    Oral presentation

  • No knotted projective plane has triple point number two
    SATOH Shin
    研究集会「４次元トポロジー」, Feb. 2008, Japanese, 鎌田 聖一, 広島大学, Domestic conference
    Oral presentation

  • On tricolorable 2-knots of triple point number four
    SATOH Shin
    The Fourth East Asian School of Knots and Related Topics, Jan. 2008, English, 河内 明夫, 東京大学・日本, International conference
    Oral presentation

  • Knotted projective plane with two triple points
    SATOH Shin
    International Conference on Topology and its Applications 2007, Dec. 2007, English, 河野 明, 京都大学・日本, International conference
    Oral presentation

  • On tricolorable 2-knots of triple point number four
    SATOH Shin
    Knotting Mathematics and Art, Nov. 2007, English, M. Saito, 南フロリダ大学・アメリカ, International conference
    Oral presentation

  • The sheet numbers of 2-knots
    SATOH Shin
    Geometric Topology Conference, Jun. 2007, English, Boju Jiang, 北京大学・中国, International conference
    Oral presentation

  • The sheet numbers of 2-knots
    SATOH Shin
    Friday Seminar on Knot Theory, Jun. 2007, Japanese, 河内 明夫, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

■ Affiliated Academic Society
  • 日本数学会

■ Research Themes
  • 曲面結び目のリスト作成と仮想結び目の不変量の研究
    佐藤 進
    日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2022 - 31 Mar. 2025

  • Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
    鎌田 聖一, 河内 明夫, 金信 泰造, 大槻 知忠, 遠藤 久顕, 佐藤 進, 安井 弘一, 大城 佳奈子, 早野 健太
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Osaka University, 01 Apr. 2019 - 31 Mar. 2024
    カンドルの代数構造に積の演算を組み込んだ代数に関する研究を行なった。このような代数構造は演算の満たすべき公理として様々な候補が考えられる。３価頂点を持つブレイドの一般化の図式に関連した構造が、一つの候補となる。これについては彩色数などの不変量があるが、直接的で幾何的な解釈を与える問題は解決されていない。前年度のフロベニウス代数の公理の図式化では、高次元化として、平面上の３価グラフとその基本変形、３次元空間内の分岐曲面が自然に現れることを見たが、今年度は少し条件を緩めた時に、４次元空間内のブレイド状の分岐曲面を考えることが自然であることがわかった。これは、仮想交点を伴うブレイドが絡み目のモーション群を用いて解釈されることに対応していて、カンドルの余次元２の部分多様体の観点での解釈により近いものといえる。充填を導入することで、佐藤やRourkeによる仮想結び目の４次元空間内のリボントーラスによる解釈のような関係が期待される。 2021年5月19日-21日に京都大学数理解析研究所で研究集会「Intelligence of Low-dimensional Topology」をオンラインで開催した。世話人は大槻知忠（分担者）と秋吉宏尚で、11件の講演と約140名（外国人1名を含む）の参加者あった。2021年11月12日-14日に大阪大学で研究集会「４次元トポロジー」をオンラインで開催した。世話人は鎌田（代表者）、安井弘一（分担者）、松本堯生で、12件の講演と84名（外国人2名を含む）の参加者があった。2021年11月25日-26日に大阪市立大学で研究集会「カンドルと対称空間」をオンラインで開催した。世話人に鎌田、大城佳奈子（分担者）が含まれ、7件の講演があった。

  • 曲面結び目の射影図による構成と不変量による分類の研究
    佐藤 進
    日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2019 - 31 Mar. 2023
    曲面結び目とは４次元ユークリッド空間に滑らかに埋め込まれた閉曲面のことであり、その射影図とは３次元ユークリッド空間に射影された像で、自己交差集合に上下の交差情報を入れたもののことである。また曲面結び目の３重点数とは、そのすべての射影図にわたる３重点の個数の最小値のことであり、これを基準にして曲面結び目の分類を与えることは、曲面結び目理論の研究において基本的かつ重要なことであると考えられる。 前年度までの研究により、３重点数が４である２次元結び目（閉曲面が２次元球面である場合の曲面結び目）の決定を行ったが、本年度はその証明で用いた手法をさらに整理し精査することにより、２次元球面とは限らない閉曲面の場合に、その３重点数を実現する射影図の自己交差集合がみたすべき必要条件を与えることができた。これを用いるとYashiro氏らによる３重点数２のトーラスの曲面結び目の非存在の結果に対する簡易な別証明を与えることができる。 また、前年度までに行った仮想結び目の３種類の交差多項式に関する一連の結果に加えて、仮想結び目の支持種数（仮想結び目の射影図を実現する閉曲面の種数の最小値）が１の場合に、トーラス上の閉曲線の回転数を利用することにより、その第三交差多項式を精密化することに成功した。これにより、通常の第三交差多項式では区別できなかった仮想結び目の対で、精密化した多項式では区別できるようになるものの存在が期待できる。

  • Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
    KAMADA SEIICHI
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Osaka City University, 01 Apr. 2014 - 31 Mar. 2019
    For an immnersed surface-link, which is a closed surface immersed in Euclidean 4-space, the notion of a normal form was introduced and it was proved that any immersed surface-link can be deformed into a normal form. Using a normal form, we obtain a method of describing immersed surface-links bu marked graph diagrams. We also introduced the notion of a ribbon-clasp surface-link as a natural generalization of a ribbon surface-link, and gave a condition for an immersed surface-link to be ribbon-clasp. The tensor product of quandles was defined, and as an application, we gave a method of describing 1-handles attaching to a surface-link. Using the tensor prodocut of a finite quandle, one can easily obtain an invariant of 1-handles attaching to a surface-link.

  • 佐藤 進
    学術研究助成基金助成金／基盤研究(C), Apr. 2016 - Mar. 2019, Principal investigator
    Competitive research funding

  • Studies of knot theory and their applications
    KAWAUCHI Akio, KAMADA Seiichi, SAKUMA Makoto, NAKANISHI Yasutaka, TANIYAMA Kouki, OOYAMA Toshiyuki, MOTEGI Kimihiko, GOUDA Hiroshi, SHIMOKAWA Koya, TERAGAITO Masakazu, SATOU Shin, TANAKA Toshihumi, IWAKIRI Masahide, CHON Inde, KISHIMOTO Kengo, OTSUKI Tomotada, SHIMIZU Ayaka
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Osaka City University, 01 Apr. 2012 - 31 Mar. 2017
    Using the knot as a key word, we have been working to encourage the development of mathematics in general, with a view of the related physics, chemistry and biology. Based on Osaka City University Mathematics Research Institute as an activity base and based on research cooperation agreements with 8 institutes in East Asia, we aimed to build a research network with Asia. We supported participation in many international or domestic regular meetings such as the satellite knot theory international conference of the Seoul International Congress of Mathematicians. Throughout these meetings, numerous important research results were obtained by a number of knot related researchers including research planning workers, which include research achievements obtaining two patents on the game "Region Select" applying the knot theory and solving a pending issue of 45 years of a ribbon 2-knot by the research representative.

  • 佐藤 進
    学術研究助成基金助成金／基盤研究(C), Apr. 2013 - Mar. 2016, Principal investigator
    Competitive research funding

  • Research on 4-dimensional topology from the viewpoint of graphics and quandle theory
    KAMADA SEIICHI, SAKUMA Makoto, MATSUMOTO Makoto, SHIMADA Ichiro, MATUMOTO Takao, TERAGAITO Masakazu, MATSUDA Hiroshi, SAEKI Osamu, OHTSUKI Tomotada, KAWAUCHI Akio, KANENOBU Taizo, MATSUMOTO Yukio, HIROSE Susumu, SHIMA Akiko, SATOH Shin
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), 01 Apr. 2009 - 31 Mar. 2014
    In order to describe a structure of a genus-2 Lefschetz fibration of a 4-manifold, we introduced a graphical method, called the chart description. Using this method, we obtained a theorem on stabilization of genus-2 Lefschetz fibrations, that is a generalization of a theorem due to D. Auroux, and a theorem due to B. Siebert and G. Tian. A symmetric quandle is a quandle with an additional structure, called a good involution. We introduced the homology theory of a symmetric quandle, and using it, we defined an invariant for surface links in 4-space. The invariant is defined even if the surface link is non-orientable. It can be used for estimation of the minimal triple number of a surface-link.

  • THE RESEARCH OF THE STRUCTURES AND INVARIANTS OF STABLE EQUIVALENCE CLASSES OF KNOTS IN THICKENED SURFACES
    KAMADA Naoko, KANENOBU Taizo, SATOH Shin, MIYAZAWA Yasuyuki
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Nagoya City University, 2010 - 2012
    We defined the quandles of the stable equivalence classes of knots in thickened surfaces (twisted knots) and gave the geometric interpretation of the quandles of twisted knots. We also introduced the multivariable polynomial invariants and the index polynomials of twisted knots and showed that they are useful to distinguish twisted knots. We coded the computer programs to makes the list of twisted knot diagrams and to calculate the invariants of twisted knots. Using the programs, we constructed thetable of twisted knots.

  • Studies of Knot Theory
    KAWAUCHI Akio, KANENOBU Taizo, TANAKA Tanaka, IWAKIRI Masahide, MORIUCHI Hiromasa, YAMAMOTO Ryousuke, TAYAMA Ikuo, SAKUMA Makoto, NAKANISHI Yasutaka, KAMADA Seiichi, TERAGAITO Masakazu, TANIYAMA Kouki, MOTEGI Kimihiko, OOYAMA Toshiyuki, GOUDA Hiroshi, HASHIMOTO Yoshitake, MASUDA Mikiya, SHIMOKAWA Koya, SATOU Shin
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Osaka City University, 2009 - 2011
    Knot theory is related to most advanced modern mathematics and also to many research fields in science. The purpose of this program was to develop、in a national scale、both education and study of an extensive knot theory on the basis of the accomplishments of the 21 COE program of Osaka City Advanced Mathematical institute. The support project of international and domestic meetings was carried out steadily、and many new findings on knot theory could be obtained. Among such research activities、unique studies of knot theory such as the publication of an English book of teaching and learning methods of knot theory in school mathematics and three patent applications of knot theory were born.

  • 佐藤 進
    科学研究費補助金／若手研究(B), 2010, Principal investigator
    Competitive research funding

  • 中西 康剛
    科学研究費補助金／基盤研究(C), 2009
    Competitive research funding

  • Applications of the Ricci flow tedimentional differential toppolog
    KUGA Kenichi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Chiba University, 2005 - 2008
    リッチ流の4次元での挙動が不安定であることの経験が得られたが、現時点で4次元における特異点生成のモデルは得られていない.しかし、リッチ流が収束するジェネリッチな構造である双曲構造と関連して、1-3価グラフから得られるある線形空間の次元を評価する公式や、双曲構造と数論との関連、また4次元中の曲面結ぴ目のある種の彩色数に関する結果が得られている.

  • 佐藤 進
    科学研究費補助金／若手研究(B), 2006, Principal investigator
    Competitive research funding

  • Topological study of Engel structures and its characteristic foliations
    INABA Takashi, HINO Yoshiyuki, KUGA Ken'ichi, TSUBOI Takashi, SATOH Shin, TAKAGI Ryoichi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Chiba University, 2002 - 2003
    An Engel structure is a maximally non-integrable 2-dimensional plane field on a 4-dimensional manifold. In this research we investigated global properties of Engel structures from the viewpoint of topology. In particular, we paid attention to the characteristic 1-dimensional foliations canonically associated to Engel structures. First, we considered the following problem posed by Gershkovich : Does there exist an Engel structure on the 4-dimensional Euclidean space whose characteristic foliation admits a compact leaf ? We affirmatively solved this problem by constructing a concrete example. We also applied the construction to obtaining Engel structures on other open 4-manifolds. This result was published in Bulletin of the Australian Mathematical Society. Next, P.Walczak, the foreign joint investigator of this research, constructed an Engel structure using an Anosov flow. The head investigator remarked that this Engel structure is essentially new. Namely, it is not isotopic to any other known examples. Thirdly, we sought 1-dimensional transversely parallelizable foliations on 4-dimensional manifolds which cannot be topologically conjugate to the characteristic foliation of any Engel structure. It is known that a characteristic foliation admits a tangential projective structure and transverse contact structure. We observed the following fact : If a compact leaf of a characteristic foliation has finite holonomy, then the projective. structure of the leaf is not affine. Using this fact we found a l-dimensional transversely parallelizable foliation which is not topologically conjugate to the characteristic foliation of any Engel structure. Finally, we initiated the study of generalizing the rigidity property of characteristic foliations of Engel structures to the cases of higher dimensional plane fields.

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