Applications of the Ricci flow tedimentional differential toppolog

• Project/Area Number: 17540063
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Chiba University
• Principal Investigator: KUGA Kenichi Chiba University, 大学院・理学研究科, 教授 (30186374)
• Co-Investigator(Kenkyū-buntansha): 稲葉 尚志 千葉大学, 大学院・理学研究科, 教授 (40125901) ; 杉山 健一 千葉大学, 大学院・理学研究科, 教授 (90206441) ; 佐藤 進 神戸大学, 大学院・理学研究科, 准教授 (90345009)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,620,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥420,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 低次元微分位相幾何学 / 微分位相幾何学 / 低次元多様体 / Ricciフロー / 4次元多様体 / Ricci flow / 可微分構造 / 4次元球面

Research Abstract

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.

Research Products

• [Journal Article] Colorings of torus knots, their twist-spuns by Alexander quandles over finite fields (2009)
  • Author(s): Sochiro. Asami and Ken'ichi Kuga
  • Journal Title: Journal of Knot Theory, Its Ramifications
  • Peer Reviewed
• [Journal Article] On geometric analogues of the Birch, Swinerton-Dyer conjecture for low dimentional hyperbolic manifolds (2009)
  • Author(s): Ken-ichi Sugivama
  • Journal Title: Contemporary Math
  • Peer Reviewed
• [Journal Article] Colorings of torus knots and their twist-spuns by Alexander quandles over finite fields, (2009)
  • Author(s): S. Asami and K. Kuga,
  • Journal Title: Jounral of Knot Theory and Its Ramifications
  • Peer Reviewed
• [Journal Article] On geometric analogues of the Birch and Swinerton-Dyer conjecture for low dimentional hyperbolic manifolds (2009)
  • Author(s): K. Sugiyama
  • Journal Title: Contemporary Math.
  • Peer Reviewed
• [Journal Article] On geometric analoges of the Birch ans Swinnerton-Dyer conjecture forlow dimensional hyperbolic manifolds (2008)
  • Author(s): Ken-ichi Sugiyama
  • Journal Title: Contemporary Mathematics (To appear)
  • Peer Reviewed
• [Journal Article] An analog of the Iwasawa conjecture for a compact hyperbolic threefold, J. Reine (2007)
  • Author(s): Ken-ichi Sugiyama
  • Journal Title: Angew. Math 613 Pages: 35-50
  • Peer Reviewed
• [Journal Article] An analog of the Iwasawa conjecture for a compact hyperbolic threefold (2007)
  • Author(s): Ken-ichi Sugiyama
  • Journal Title: J. Reine. Angew. Math. 613 Pages: 35-50
  • Peer Reviewed
• [Journal Article] On some formulas in combinatorial computation of uni-trivalent graphs (2006)
  • Author(s): Kazutaka Hanawa and Ken'ichi Kuga
  • Journal Title: Indian Journal fo Pure, Applied Mathematics 37No.2 Pages: 75-88
  • Peer Reviewed
• [Journal Article] On rigidity of submanifolds tangent to nonintegrable distributions (2006)
  • Author(s): Takashi Inaba
  • Journal Title: Proceedings fo the International Conference FOLIATIONS 2005 Pages: 203-214
  • Peer Reviewed
• [Journal Article] On some formulas in combinatorial computation of uni-trivalent graphs (2006)
  • Author(s): Kazutaka Hanawa, Ken'ichi Kuga
  • Journal Title: Indian Journal of Pure and Applied Mathematics 37 No.2 Pages: 75-88
• [Journal Article] On rigidity of submanifolds tangent to nonintegrable distributions (2006)
  • Author(s): Takashi Inoda
  • Journal Title: Proceeding of the International Conference FOLIATIONS 2005 Pages: 203-214
• [Journal Article] On the Hodge conjecture and the Tate conjecture for Hilbert schemes of an abelian surface (2006)
  • Author(s): Ken-ichi Sugiyama
  • Journal Title: Mathematische Nachrichten 279 Pages: 213-231
• [Journal Article] On the Hodge conjecture and the Tate conjecture for the Hilbert schemes of an abelian surface. (2006)
  • Author(s): Sugiyama, Ken-ichi
  • Journal Title: Math.Nachr. 279 no.1-2 Pages: 217-231
• [Journal Article] Non-additivity for triple point numbers on the connected sum of surface-knots, (2005)
  • Author(s): Satoh, Shin
  • Journal Title: Proc.Amer.Math.Soc. 133 Pages: 613-616