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曲面に付随する複体および写像類群の計算可能性と大域幾何

Research Project

Project/Area Number06F06034
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section外国
Research Field Geometry
Research InstitutionTokyo Institute of Technology
Host Researcher 小島 定吉  Tokyo Institute of Technology, 大学院・情報理工学研究科, 教授
Foreign Research Fellow SHACKLETON K. J.  東京工業大学, 大学院・情報理工学研究科, 外国人特別研究員
SHACKLETON K.J.  東京工業大学, 大学院・情報理工学研究科, 外国人特別研究員
Project Period (FY) 2006 – 2008
Project Status Completed(Fiscal Year 2008)
Budget Amount *help
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 2008 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 2007 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 2006 : ¥700,000 (Direct Cost : ¥700,000)
Keywords幾何学的群論 / 双曲幾何 / タイヒミュラー理論 / 結び目理論 / 写像類群 / カーブグラフ / パンツグラフ
Research Abstract

本研究は,日本学術振興会外国人特別研究員であるKenneth J.Shackleton氏と共同で,曲面のタイヒミュラー空間の大域幾何の理解を深め,3次元多様体の研究への応用,とくに写像柱の体積との関係について知見を得ることを目指している.今年度は最終年度で,しかも8月一杯でShackleton氏が特別研究員から離任したため期間が短かったが,日常的な研究打ち合わせを行い,タイヒミュラー空間のヴェイユ・ピータンソン幾何に関する理解を深めることができた.とくに,擬アノソフ写像のエントロピーと対応する写像柱の体積は,幾何の有界性を仮定すれば比較可能であることが証明できた。
一方,Shackleton氏自身はパンツグラフ上の2点間の距離は計算可能かという大目標に取り組んでいるが,前年度末にほぼ完成させた2点穴空きトーラスと5点穴空き球面についての証明を精査し,論文を完成させるべく議論のポリシュを図った。また,その過程で自らたどり着いた「パンツグラフの中で自然に定義される余次元一定の部分グラフは前測地的」という予想に取り組み,地に足の着いた進展を得ている。
これらの業績が評価され,Shackleton氏は東京大学の数物連携宇宙研究機構(IPMU)のポスドクに採用され,昨年の10月半ばから日本での足掛け4年目の研究生活を始めている。

Report

(3results)
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • 2006 Annual Research Report

Research Products

(15results)

All 2009 2008 2007 2006 Other

All Journal Article Presentation Remarks

  • [Journal Article] Entropy versus volume for pseudo-Anosovs2009

    • Author(s)
      E. Kin, S. Kojima, M. Takasawa
    • Journal Title

      Experimental Mathematics (In press)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the distance between two Seifert surfaces of a knot2009

    • Author(s)
      M. Sakuma, K. Shackleton
    • Journal Title

      Osaka J. Math. 46

      Pages : 203-221

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Totally geodesic subgraphs of the pants complex2008

    • Author(s)
      Aramayona, Parlier, Shackleton
    • Journal Title

      Math. Res. Lett. 15

      Pages : 309-320

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the distance between two Seifert surfaces of a knot2008

    • Author(s)
      Shackleton, Sakuma
    • Journal Title

      to appear in Osaka J.Math (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Totally geodesic subgraphs of the pants complex2008

    • Author(s)
      Shackleton, Aramayona, Parlier
    • Journal Title

      to appear in Math.Res.Lett. (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free subgroups of surface mapping class groups2007

    • Author(s)
      Shackleton, Anderson, Aramayona
    • Journal Title

      Conform.Geom.Dyn. 11

      Pages : 44-55

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Combinatorial rigidity in curve complexes and mapping class groups2007

    • Author(s)
      Kenneth J.Shackleton
    • Journal Title

      Pacifc Journal of Mathematics 230

      Pages : 217-232

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Free subgroups of surface mapping class groups2007

    • Author(s)
      Kenneth J.Shackleton
    • Journal Title

      Conformal Geometry and Dynamics 11(To appear)

      Pages : 44-45

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures and uniformization2006

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      Pacific Journal of Mathematics 225

      Pages : 287-300

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures : a survey2006

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      London Math.Soc., Lecture Note Series 329

      Pages : 337-353

    • Related Report
      2006 Annual Research Report
  • [Journal Article] An obstruction to the strong relative hyperbolicity of a group

    • Author(s)
      Kenneth J.Shackleton
    • Journal Title

      Journal of Group Theory (掲載決定)(To appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Uniformly exponential growth and mapping class groups of surfaces

    • Author(s)
      Kenneth J.Shackleton
    • Journal Title

      Proceedings of the Ahlfors-Bers Colloquium (掲載決定)(To appear)

    • Related Report
      2006 Annual Research Report
  • [Presentation] Entropy vs Volume2008

    • Author(s)
      Sadayoshi Kojima
    • Organizer
      KIAS Workshop on Hyperbolic Geometry and Related Topics
    • Place of Presentation
      Korean Institute for Advanced Study
    • Year and Date
      2008-12-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] on the coarse geomty on the weil-Petersson metric2007

    • Author(s)
      Shackleton, K.J.
    • Organizer
      Symposium on low dimensionil Geometry and Topology
    • Place of Presentation
      Warwick University(UK)
    • Year and Date
      2007-07-19
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL
      http://www.is.titech.ac.jp/~sadayosi/
    • Related Report
      2008 Annual Research Report

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

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