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Applications of the Ricci flow tedimentional differential toppolog

Research Project

Project/Area Number 17540063
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionChiba 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 *help
¥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.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (14 results)

All 2009 2008 2007 2006 2005

All Journal Article (14 results) (of which Peer Reviewed: 9 results)

  • [Journal Article] Colorings of torus knots, their twist-spuns by Alexander quandles over finite fields2009

    • Author(s)
      Sochiro. Asami and Ken'ichi Kuga
    • Journal Title

      Journal of Knot Theory, Its Ramifications

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On geometric analogues of the Birch, Swinerton-Dyer conjecture for low dimentional hyperbolic manifolds2009

    • Author(s)
      Ken-ichi Sugivama
    • Journal Title

      Contemporary Math

    • Related Report
      2008 Final Research Report
    • 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

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On geometric analogues of the Birch and Swinerton-Dyer conjecture for low dimentional hyperbolic manifolds2009

    • Author(s)
      K. Sugiyama
    • Journal Title

      Contemporary Math.

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On geometric analoges of the Birch ans Swinnerton-Dyer conjecture forlow dimensional hyperbolic manifolds2008

    • Author(s)
      Ken-ichi Sugiyama
    • Journal Title

      Contemporary Mathematics (To appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An analog of the Iwasawa conjecture for a compact hyperbolic threefold, J. Reine2007

    • Author(s)
      Ken-ichi Sugiyama
    • Journal Title

      Angew. Math 613

      Pages: 35-50

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An analog of the Iwasawa conjecture for a compact hyperbolic threefold2007

    • Author(s)
      Ken-ichi Sugiyama
    • Journal Title

      J. Reine. Angew. Math. 613

      Pages: 35-50

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On some formulas in combinatorial computation of uni-trivalent graphs2006

    • Author(s)
      Kazutaka Hanawa and Ken'ichi Kuga
    • Journal Title

      Indian Journal fo Pure, Applied Mathematics 37No.2

      Pages: 75-88

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On rigidity of submanifolds tangent to nonintegrable distributions2006

    • Author(s)
      Takashi Inaba
    • Journal Title

      Proceedings fo the International Conference FOLIATIONS 2005

      Pages: 203-214

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On some formulas in combinatorial computation of uni-trivalent graphs2006

    • Author(s)
      Kazutaka Hanawa, Ken'ichi Kuga
    • Journal Title

      Indian Journal of Pure and Applied Mathematics 37 No.2

      Pages: 75-88

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On rigidity of submanifolds tangent to nonintegrable distributions2006

    • Author(s)
      Takashi Inoda
    • Journal Title

      Proceeding of the International Conference FOLIATIONS 2005

      Pages: 203-214

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the Hodge conjecture and the Tate conjecture for Hilbert schemes of an abelian surface2006

    • Author(s)
      Ken-ichi Sugiyama
    • Journal Title

      Mathematische Nachrichten 279

      Pages: 213-231

    • Related Report
      2006 Annual Research Report
  • [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

    • Related Report
      2005 Annual Research Report
  • [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

    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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