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Low-dimensional topological invariants, hyperbolic volume and Perelman invariants

Research Project

Project/Area Number 21540069
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 Ken-ichi  千葉大学, 理学(系)研究科(研究院), 教授 (30186374)

Co-Investigator(Kenkyū-buntansha) INABA Takashi  千葉大学, 大学院理学研究科, 教授 (40125901)
SUGIYAMA Ken-ichi  千葉大学, 大学院理学研究科, 教授 (90206441)
Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords低次元位相不変量 / 双曲体積 / 低次元多様体 / コバノフホモロジー / 4次元多様体 / リッチ流 / Ricci流 / 微分トポロジー / 低次元トポロジー / 位相不変量 / ペレルマン不変量
Research Abstract

We investigated the possibility of applying the technique of Hamilton's Ricci flow to the understanding of the topology of 4 dimensional manifolds, or more generally, to the understanding of various topological invariants in low-dimensional topology. While in dimension three, the formation of singularities is well understood due to the works of Hamilton and Perelman,in dimension 4, the singularity seems unstable with respect to the initial metiric, which eventually prevented our systematic understanding of the formation in dimension 4 during this period of study. Some peripheral computation concerning Khovanov homology of some links were performed.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (9 results)

All 2014 2012 2011 2010 2009

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (1 results)

  • [Journal Article] On a generalization of Deuring's results2014

    • Author(s)
      Sugiyama, K
    • Journal Title

      Finite Fields and Their Applications

      Volume: 26C Pages: 69-85

    • DOI

      10.1016/j.ffa.2013.11.004

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Normally contracting Lie group actions2012

    • Author(s)
      Inaba, Takashi; Matsumoto, Shigenori; Mitsumatsu, Yoshihiko
    • Journal Title

      Topology Appl

      Volume: 159, no. 5 Issue: 5 Pages: 1334-1338

    • DOI

      10.1016/j.topol.2011.12.012

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Normally contracting Lie group actions2012

    • Author(s)
      T.Inaba, S.Matsumoto, Y.Mitsumatsu
    • Journal Title

      Topology Appl.

      Volume: 159 Pages: 1334-1338

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Countable limit sets of unimodal maps2010

    • Author(s)
      Inaba, T.; Kano, Y
    • Journal Title

      J. Dyn. Control Syst

      Volume: 16, no. 3 Issue: 3 Pages: 319-328

    • DOI

      10.1007/s10883-010-9095-7

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Countable limit sets of unimodal maps2010

    • Author(s)
      T.Inaba, Y.Kano
    • Journal Title

      Journal of Dynamical Control Systems

      Volume: 16-3 Pages: 319-328

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Colorings of torus knots and their twist-spuns by Alexander quandles over finite fields2009

    • Author(s)
      Asami,S; Kuga, K
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 18巻no. 9 Issue: 09 Pages: 1259-1270

    • DOI

      10.1142/s0218216509007452

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Colorings of torus knots and their twist-spuns by Alexander quandles over finite fields2009

    • Author(s)
      S.Asami, K.Kuga
    • Journal Title

      Journal of Knot Theory and Its Ramifications Vol.18 No.9

      Pages: 1529-1270

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On geometric analogues of the Iwasawa conjecture for a hyperbolic threefold2009

    • Author(s)
      K.Sugiyama
    • Journal Title

      Adv. Stud. in Pure Mathematics 484

      Pages: 267-286

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] An attempt to define entropy of plane fields2011

    • Author(s)
      稲葉尚志
    • Organizer
      Plane Fields on Manifolds and Diffeomorphisms Groups 2011
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2011-11-02
    • Related Report
      2013 Final Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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