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Research on spaces of non-positive curvature with group actions and Coxeter groups

Research Project

Project/Area Number 21740037
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionShizuoka University (2011-2012)
Utsunomiya University (2009-2010)

Principal Investigator

HOSAKA Tetsuya  静岡大学, 理学部, 准教授 (50344908)

Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords幾何学的群論 / 位相幾何学 / CAT(0)空間 / CAT(0)群 / Coxeter群 / Davis複体 / 境界 / 再構成可能グラフ / flag complex / quasi-isometry / equivariant同相 / equivariant 同相 / asymptotic次元 / Higson corona / 次元
Research Abstract

I have obtained some results on CAT(0) groups, CAT(0) spaces, their boundaries and Coxeter groups. First, I proved a "splitting theorem" for CAT(0) spaces, and obtained that products of rigid CAT(0) groups are also rigid CAT(0). Next, I had some results on equivariant-homeomorphisms of boundaries of CAT(0) groups. Also I obtained results on algebraic rigidity of Coxeter groups and on graph theory by investigating corresponding Coxeter groups.

Report

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

    (27 results)

All 2013 2012 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (12 results) Remarks (1 results)

  • [Journal Article] On a new class of rigid Coxeter group2013

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: (印刷中)

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups2013

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Osaka Journal of Mathematics

      Volume: (印刷中)

    • NAID

      120005830508

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic dimension and boundary dimension of proper CAT(0) spaces2012

    • Author(s)
      Naotsugu Chinen and Tetsuya Hosaka
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 36 Pages: 185-191

    • NAID

      120006582859

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] n splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature2012

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Mathematische Zeitschrift

      Volume: 272 Issue: 3-4 Pages: 1037-1050

    • DOI

      10.1007/s00209-011-0972-x

    • Related Report
      2012 Annual Research Report 2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces2012

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Rocky Mountain Journal of Mathematics

      Volume: Vol 42 Pages: 1207-1214

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On non-sensitive homeomorphisms of the boundary of a proper cocompact CAT(0) space2011

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Journal of Mathematical Sciences, The University of Tokyo

      Volume: 18 Pages: 491-504

    • NAID

      120006906073

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On boundaries of Coxeter groups and topological fractal structures2011

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 35 Pages: 153-160

    • NAID

      120006312317

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Non-Sensitive Homeomorphisms of the Boundary of a Proper Cocompact CAT(0) Spaces2011

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Journal of Mathematical Sciences, the University of Tokyo

      Volume: 18 Pages: 491-504

    • NAID

      120006906073

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] CAT(0) groups and Coxeter groups whose boundaries are scrambled sets2010

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 214 Pages: 919-936

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic dimension of proper CAT(0) spaces that are homeomorphic to the plane2010

    • Author(s)
      Journal of Pure and Applied Algebra
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 53 Pages: 629-638

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane2010

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

      Canadian Mathematical Bulletin

      Volume: 53 Pages: 629-638

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] CAT(0)groups and Coxeter groups whose boundaries are scrambled sets2010

    • Author(s)
      T.Hosaka
    • Journal Title

      Journal of Pure and Applied Algebra 214

      Pages: 919-936

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a new class of rigid Coxeter group

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: (印刷中)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups

    • Author(s)
      Tetsuya Hosaka
    • Journal Title

      Osaka Journal of Mathematics

      Volume: (印刷中)

    • NAID

      120005830508

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] On structure of CAT(0) groups2012

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般位相幾何学および幾何学的トポロジーの現状と諸問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-09-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Topological fractal structures of boundaries of Coxeter groups and CAT(0) groups2012

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「力学系とその周辺分野の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-07-11
    • Related Report
      2012 Final Research Report
  • [Presentation] On local connectivity of boundaries of CAT(0) spaces2011

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般及び幾何学的トポロジーとその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-10-18
    • Related Report
      2012 Final Research Report
  • [Presentation] On local connectivity of boundaries of CAT(0) spaces2011

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般及び幾何学的トポロジーとその応用」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2011-10-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] On equivariant homeomorphisms of boundaries of CAT(0) groups2011

    • Author(s)
      Tetsuya Hosaka
    • Organizer
      Rigidity School, Nara 2010/2011
    • Place of Presentation
      奈良商工会議所
    • Year and Date
      2011-03-05
    • Related Report
      2012 Final Research Report
  • [Presentation] On equivariant homeomorphisms of boundaries of CAT(0)groups2011

    • Author(s)
      保坂哲也
    • Organizer
      Rigidity School, Nara 2010/2011
    • Place of Presentation
      奈良商工会議所
    • Year and Date
      2011-03-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] On equivariant homeomorphisms of boundaries of CAT(0) groups2010

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2012 Final Research Report
  • [Presentation] On equivariant homeomorphisms of boundaries of CAT(0)groups2010

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Coxeter群のrank-one isometryとその境界について2010

    • Author(s)
      保坂哲也
    • Organizer
      第45回位相空間論シンポジウム
    • Place of Presentation
      大阪府立大学理学部サイエンスホール
    • Year and Date
      2010-06-05
    • Related Report
      2012 Final Research Report
  • [Presentation] On rank-one isometries of right-angled Coxeter groups and their boundaries2009

    • Author(s)
      保坂哲也
    • Organizer
      数理解析研究所研究集会「一般位相幾何学及び幾何学的トポロジーに関する研究」
    • Place of Presentation
      京都大学楽友会館
    • Year and Date
      2009-10-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Topological fractal structures of boundaries of Coxeter groups and CAT(0) groups

    • Author(s)
      保坂 哲也
    • Organizer
      数理解析研究所研究集会「力学系とその周辺分野の研究」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2012 Annual Research Report
  • [Presentation] On structure of CAT(0) groups

    • Author(s)
      保坂 哲也
    • Organizer
      数理解析研究所研究集会「一般位相幾何学および幾何学的トポロジーの現状と諸問題」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://www.sci.shizuoka.ac.jp/~math/staffs/hosaka.html

    • Related Report
      2012 Final Research Report

URL: 

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

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