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Study on Coxeter groups and spaces of non-positive curvature

Research Project

Project/Area Number 18740025
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionUtsunomiya University

Principal Investigator

HOSAKA Tetsuya  Utsunomiya University, 教育学部, 准教授 (50344908)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,170,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords位相幾何学 / 幾何学的群論 / Coxeter群 / CAT(0)空間 / CAT(0)群 / Davis複体 / 境界 / asymptotic次元 / コクセター群 / 攪拌集合 / 群の境界
Research Abstract

群作用のある非正曲率空間(CAT(0)空間)の「境界」とよばれる空間の研究, および, 鏡映によって生成されるCoxeter群とよばれる群の作用するDavis複体とよばれるCAT(0)空間の境界の研究を行った。「境界」は興味深い研究対象でありながら一般に非常に複雑な構造を持つために扱うのが困難であるが, 本研究では, 力学系のカオス理論の考え方を導入し, 研究成果を得た。また, 未解決で重要な問題が残されているCAT(0)空間とCAT(0)群のasymptotic次元とよばれる次元に関して, 沖縄高専の知念直紹氏との共同研究により, 研究成果を得ている。

Report

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

    (14 results)

All 2009 2008 2007 2006 Other

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Presentation (9 results)

  • [Journal Article] Minimality of the boundary of a right-angled Coxeter system2009

    • Author(s)
      T. Hosaka
    • Journal Title

      Proceedings of the American Mathematical Society 137

      Pages: 899-910

    • Related Report
      2008 Annual Research Report 2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to the plane2009

    • Author(s)
      N. Chinen and T. Hosaka
    • Journal Title

      Canadian Mathematical Bulletin (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dense subsets of boundaries of CAT(0) groups2008

    • Author(s)
      T. Hosaka
    • Journal Title

      Houston Journal of Mathematics 34, no.4

      Pages: 1057-1063

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to the plane

    • Author(s)
      N. Chinen and T. Hosaka
    • Journal Title

      Canadian Mathematical Bulletin (印刷中)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dense subsets of boundaries of CAT(0) groups

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Houston Journal of Mathematics (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Presentation] On isometry groups of CAT(0) spaces2009

    • Author(s)
      T. Hosaka
    • Organizer
      「同相群とその周辺」研究会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2009-02-21
    • Related Report
      2008 Final Research Report
  • [Presentation] On isometry groups of CAT(0)spaces2009

    • Author(s)
      保坂哲也
    • Organizer
      「同相群とその周辺」研究会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2009-02-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Minimality and scrambled sets of boundaries of CAT(0) groups2008

    • Author(s)
      T. Hosaka
    • Organizer
      リーマン幾何と幾何解析
    • Place of Presentation
      筑波大学
    • Year and Date
      2008-02-19
    • Related Report
      2008 Final Research Report
  • [Presentation] On the boundary of a CAT(0) space on which a group acts geometrically2008

    • Author(s)
      T. Hosaka
    • Organizer
      リーマン面不連続群論研究集会 -Conference on Riemann surfaces and discrete groups-
    • Place of Presentation
      岡山大学
    • Year and Date
      2008-01-14
    • Related Report
      2008 Final Research Report
  • [Presentation] Minimality and scrambled sets of boundaries of CAT(0) groups2007

    • Author(s)
      T. Hosaka
    • Organizer
      International Conference on Topology and its Applications 2007 at Kyoto
    • Place of Presentation
      京都大学
    • Year and Date
      2007-12-05
    • Related Report
      2008 Final Research Report
  • [Presentation] Minimality and scrambled sets of boundaries of CAT (0) groups2007

    • Author(s)
      保坂 哲也
    • Organizer
      International Conference on Topology and its Applications 2007 at Kyoto
    • Place of Presentation
      京都大学理学部3号館
    • Year and Date
      2007-12-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] CAT(0) groups whose boundaries are scrambled sets, 一般および幾何学的トポロジーの現状と諸問題2007

    • Author(s)
      T. Hosaka
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-18
    • Related Report
      2008 Final Research Report
  • [Presentation] On minimality of the boundary of a Coxeter system, 一般位相幾何学及び幾何学的トポロジーとその応用2007

    • Author(s)
      T. Hosaka
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Minimality of the boundary of a right-angled Coxeter system2006

    • Author(s)
      T. Hosaka
    • Organizer
      Rigidity School, Nagoya 2006
    • Place of Presentation
      名古屋大学
    • Year and Date
      2006-09-28
    • Related Report
      2008 Final Research Report

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

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