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Research of 3-manifolds by topological and hyperbolic geometric method

Research Project

Project/Area Number 18540097
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Metropolitan University

Principal Investigator

SOMA Teruhiko  Tokyo Metropolitan University, 大学院・理工学研究科, 教授 (50154688)

Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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: ¥900,000 (Direct Cost: ¥900,000)
Keywords位相幾何学 / 微分トポロジー / hyperbolic 3-manifolds / Ending Lamination Con jecture / curve complex / geometric limits / Seifert fibered space / Kleinian groups / 3次元多様体 / 双曲幾何学 / クライン群 / 曲線複体 / 双曲多様体 / エンディング・ラミネーション / ending lamination / quasi-Fuchsian groups / Marden's conjecture / ruled wrappings / Seifert fibered spaces / Lozi maps / shadowing property
Research Abstract

I introduced the notion of ruled wrappings and by using it gave a simple alternative proof of Marden's conjecture. We completed the geometric classification of geometric limits hyperbolic manifolds which are given by geometric limits of sequences of hyperbolic 3-manifolds with fundamental groups isometric to compact surface groups. In particular, we proved that, if these two geometric manifolds are homeomorphic and have the same end invariants, the homeomorphism is properly homotopic to an isometry.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (30 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (14 results) (of which Peer Reviewed: 12 results) Presentation (12 results) Remarks (4 results)

  • [Journal Article] 位相的クライン群論の最近の話題2010

    • Author(s)
      相馬輝彦
    • Journal Title

      数学(論説) Vol.62

      Pages: 18-39

    • NAID

      130004558898

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Heterodimensional tangencies on cycles leading to strange attractors2010

    • Author(s)
      S. Kiriki, Y. Nishizawa, T. Soma
    • Journal Title

      Discrete Conti. Dynam. Sys. Vol.27

      Pages: 285-300

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 位相的クライン群論の最近の話題2010

    • Author(s)
      相馬輝彦
    • Journal Title

      数学(論説) 62

      Pages: 18-39

    • NAID

      130004558898

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heterodimensional tangencies on cycles leading to strange attractors2010

    • Author(s)
      S.Kiriki, Y.Nishizawa, T. Soma
    • Journal Title

      Discrete Conti. Dynam. Sys. 27

      Pages: 285-300

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies2008

    • Author(s)
      S. Kiriki, T. Soma
    • Journal Title

      Nonlinearity Vol.21

      Pages: 1105-1140

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies2008

    • Author(s)
      S. Kiriki, T. Soma
    • Journal Title

      Nonlinearity 21

      Pages: 1105-1140

    • Related Report
      2008 Annual Research Report 2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Parameter-shifted shadowing property of Lozi maps2007

    • Author(s)
      Shin Kiriki and Teruhiko Soma
    • Journal Title

      Dynamical Systems 22

      Pages: 351-363

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of ruled wrappings in hyperbolic 3-manifolds2006

    • Author(s)
      T. Soma
    • Journal Title

      Geom. Topol. Vol.10

      Pages: 1173-1184

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of ruled wrappings in hyperbolic 3-manifolds2006

    • Author(s)
      T. Soma
    • Journal Title

      Geom. Topol 10

      Pages: 1173-1184

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Existence of ruled wrappings in hyperbolic 3-manifolds2006

    • Author(s)
      TeruhikoSoma
    • Journal Title

      Geometry and Topology 10

      Pages: 1173-1184

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Scott's rigidity theorem for Seifert fibered spaces; revisited2006

    • Author(s)
      Teruhiko Soma
    • Journal Title

      TransactionsofAmericanMathematicalSociety 358

      Pages: 4057-4070

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 位相的クライン群論の最近の話題

    • Author(s)
      相馬輝彦
    • Journal Title

      数学・論説 (掲載決定)

    • NAID

      130004558898

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] 論説 : 位相的クライン群論の最近の話題

    • Author(s)
      相馬 輝彦
    • Journal Title

      数学 掲載決定

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies

    • Author(s)
      Shin Kiriki and Teruhiko Soma
    • Journal Title

      Nonlinearity (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Existence of generic cubic homoclinic tangencies for Henon maps2009

    • Author(s)
      T. Soma
    • Organizer
      NCTS Dynamics Day-focusing on nonhyperbolic systems
    • Place of Presentation
      Nat'l Chiao Tung Univ., TAIWAN
    • Year and Date
      2009-11-06
    • Related Report
      2009 Final Research Report
  • [Presentation] Existence of generic cubic homoclinic tangencies for Henon maps2009

    • Author(s)
      T.Soma
    • Organizer
      NCTS Dynamics Day-focusing on ono-hyperbolic systems
    • Place of Presentation
      Nat'l Chiao Tung Univ., TAIWAN
    • Year and Date
      2009-11-06
    • Related Report
      2009 Annual Research Report
  • [Presentation] 幾何的極限とエンディング・ラミネーション予想2009

    • Author(s)
      相馬輝彦
    • Organizer
      日本数学会年会・トポロジー分科会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2009 Final Research Report
  • [Presentation] 幾何的極限とエンディング・ラミネーション予想2009

    • Author(s)
      相馬輝彦
    • Organizer
      日本数学会年会・トポロジー分科会・特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report 2008 Self-evaluation Report
  • [Presentation] Geometric limits and Ending Lamination Conjecture2009

    • Author(s)
      相馬輝彦
    • Organizer
      「リーマン面・不連続群論」研究集会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-01-12
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] metry and topology of geometric limits2007

    • Author(s)
      T. Soma
    • Organizer
      Topics in Teichmuller Theory and Kleinian Groups
    • Place of Presentation
      MSRI, Berkele, USA
    • Year and Date
      2007-11-13
    • Related Report
      2009 Final Research Report
  • [Presentation] Geometry and topology of geometric limits2007

    • Author(s)
      T. Soma
    • Organizer
      Topics in Teichmuller Theory and Kleinian Groups
    • Place of Presentation
      MSRI, Berkeley, USA.
    • Year and Date
      2007-11-13
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Geometry and topology of geometric limits2007

    • Author(s)
      Teruhiko Soma
    • Organizer
      Topics in Teichmuller Theory and Kleinian Groups
    • Place of Presentation
      MSRI, Berkeley, USA
    • Year and Date
      2007-11-13
    • Related Report
      2007 Annual Research Report
  • [Presentation] Ahlfors' measure problem for geometric limit Kleinian groups2007

    • Author(s)
      T. Soma
    • Organizer
      Lars Ahlfors Centennial Celebration
    • Place of Presentation
      Univ. of Helsinki, FINLAND
    • Year and Date
      2007-08-24
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Geometric limits of quasi-Fuchsian groups2007

    • Author(s)
      T. Soma
    • Organizer
      Hyperbolic Structures on 3-Manaifolds and Large Scale Geometry of Teichmuller Space
    • Place of Presentation
      Univ. of Warwick, ENGLAND
    • Year and Date
      2007-07-16
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Cubic dynamics on the Henon family2007

    • Author(s)
      相馬輝彦
    • Organizer
      2006年度冬の力学系研究集会
    • Place of Presentation
      東京大学
    • Year and Date
      2007-01-07
    • Related Report
      2009 Final Research Report
  • [Presentation] Geometric limits of quasi- Fuchsian groups

    • Author(s)
      T. Soma
    • Organizer
      Hyperbolic Structures on 3-Manaifolds and Large Scale Geometry of Teichmuller Space
    • Place of Presentation
      Univ. of Warwick, ENGLAND
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.comp.metro-u.ac.jp/~tsoma/

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.comp..metro-u.ac.jp/~tsoma/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.comp.metro-u.ac.jp/~tsoma/

    • Related Report
      2008 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.comp.metro-u.ac.jp/~tsoma/

    • Related Report
      2008 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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