Diagrammatic surface-knot theory

• Project/Area Number: 18740026
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kobe University
• Principal Investigator: SATOH Shin Kobe University, 大学院理学研究科, 准教授 (90345009)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,800,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000)
• Keywords: 曲面結び目 / 射影図 / 3重点数 / シート数 / ブレイド指数 / カンドル / 2次元結び目 / 曲画結び目 / ツイストスパン / スパン結び目

Research Abstract

4次元空間内の曲面(曲面結び目)がどれ程複雑に絡まっているかを定量的に表す指標である、シート数および三重点数に関して、カンドル彩色やカンドル不変量との関係を明らかにした。

Research Products

• [Journal Article] Triviality of a 2-knot with one or two sheets (2009)
  • Author(s): S. Satoh
  • Journal Title: Kyushu J. Math 63
  • Peer Reviewed
• [Journal Article] Triviality of a 2-knot with one or two sheets (2009)
  • Author(s): Shin Satoh
  • Journal Title: Kyushu J. Math 63 Pages: 1-14
  • Peer Reviewed
• [Journal Article] Sheet number and quandle-colored 2-knot (2009)
  • Author(s): Shin Satoh
  • Journal Title: J. Math. Soc. Japan 2 Pages: 1-28
  • Peer Reviewed
• [Journal Article] A note on the shadow cocycle invariant of a knot with a base point (2007)
  • Author(s): S. Satoh
  • Peer Reviewed
• [Journal Article] A note on the shadow cocyle invariant of a knot with a base point (2007)
  • Author(s): Shin Satoh
  • Journal Title: J. Knot Theory Ramifications Vol. 16 No. 7 Pages: 959-967
  • Peer Reviewed
• [Journal Article] Ribbon concordance of surface-knots via quandle cocycle invariants (2006)
  • Author(s): C. J. Scott, M. Saito, and S. Satoh
  • Journal Title: J. Aust. Math. Soc 80
  • Peer Reviewed
• [Journal Article] Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers, Proc (2006)
  • Author(s): C. J. Scott, M. Saito, and S. Satoh
  • Journal Title: Amer. Math. Soc 134
  • Peer Reviewed
• [Journal Article] Ribbon concordance of surface-knots via quandle cocycle invariants (2006)
  • Author(s): Shin Satoh
  • Journal Title: J. Aust. Math. Soc. vol. 80, no. 1 Pages: 131-147
• [Journal Article] Ribbon moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers (2006)
  • Author(s): Shin Satoh
  • Journal Title: Proc. Amer. Math. Soc. vol. 134, no. 9 Pages: 2779-2783
• [Journal Article] The braid index is not additive for the connected sum of 2-knots (2006)
  • Author(s): Shin Satoh
  • Journal Title: Trans. Amer. Math. Soc. vol. 358, no. 12 Pages: 5425-5439
• [Journal Article] A lower bound for the number of Reidemeister moves of type III (2006)
  • Author(s): Shin Satoh
  • Journal Title: Topology Appl. vol. 153, no. 15 Pages: 2788-2794
• [Presentation] 非自明2次元結び目のシート数は4以上 (2009)
  • Author(s): 佐藤進
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-28
• [Presentation] 非自明2次元結び目のシート数は4以上 (2009)
  • Author(s): 佐藤進
  • Organizer: 日本数学会2009年度年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] 5彩色可能な結び目の4色で塗られる射影図 (2008)
  • Author(s): 佐藤進
  • Organizer: 日本数学会2008年度秋季総合分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] 三重点数4の3彩色可能な2次元結び目について (2008)
  • Author(s): 佐藤進
  • Organizer: 日本数学会トポロジー分科会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-23
• [Presentation] 5彩色可能な結び目の4色で塗られる射影図 (2008)
  • Author(s): 佐藤進
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東京工業大学
• [Presentation] 非自明な基本カンドルをもつ2次元結び目のシート数 (2008)
  • Author(s): 佐藤進
  • Organizer: 日本数学会年会
  • Place of Presentation: 埼玉大学
• [Presentation] 二次元リボン絡み目の単純射影図について (2006)
  • Author(s): 佐藤進
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪市立大学.