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Applications of global coordinate systems for the representation spaces of punctured surface groups

Research Project

Project/Area Number 22540191
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionShimane University

Principal Investigator

NAKANISHI Toshihiro  島根大学, 総合理工学研究科, 教授 (00172354)

Co-Investigator(Renkei-kenkyūsha) SAKUMA Makoto  広島大学, 理学研究科, 教授 (30178602)
MOROSAWA Shunsuke  高知大学, 理学部, 教授 (50220108)
MIYACHI Hideki  大阪大学, 理学研究科, 准教授 (40385480)
Research Collaborator NAKAMURA Gou  愛知工業大学, 工学部, 准教授 (50319208)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsタイヒミュラー空間 / リーマン面 / 離散群 / 写像類群 / 双曲幾何学 / フックス群 / 双曲幾何 / マクシェイン型恒等式 / 不連続群
Research Abstract

R.C.Penner’s lambda length coordinate system for the Teichmuller space of a punctured surface has many applications to complex analysis, differential geometry, topology and to mathematical physics. We introduced a complexification of Penner’s coordinates in order to parametrize SL(2,C) representation spaces of punctured surface groups. The complex coordinates are applied to the theories of Kleinian groups, hyperbolic 3-manifolds, mapping class groups, complex dynamics and number theory.

Report

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

    (22 results)

All 2013 2012 2011 2010 Other

All Journal Article (8 results) (of which Peer Reviewed: 6 results) Presentation (14 results)

  • [Journal Article] Trace parameters for Teichmuller space of genus 2 surfaces and mapping class group, Annales Universitatis Mariae Curie-Sklodowska2013

    • Author(s)
      中村豪,中西敏浩
    • Journal Title

      Sectio A

      Volume: Vol.67 Issue: 1 Pages: 35-44

    • DOI

      10.2478/v10062-012-0020-2

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Parametrizations of some Teichmuller spaces by trace functions2013

    • Author(s)
      中村豪,中西敏浩
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: Vol.17 Pages: 47-57

    • URL

      http://www.ams.org/publications/journals/journalsframework/ecgd

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Parametrizations od some Teichmuller spaces by trace functions2013

    • Author(s)
      Gou Nakamura
    • Journal Title

      Conformal Geometry and Dynamics

      Volume: 17 Pages: 47-57

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parametrizations of some Teichmuller spaces by tracefunctions2012

    • Author(s)
      中村豪,中西敏浩
    • Journal Title

      数理解析研究所講究録

      Volume: Vol.1777 Pages: 62-74

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/kokyuroku.html

    • Related Report
      2012 Final Research Report
  • [Journal Article] Paramettrizations of Teichmuller spaces by trace functions2012

    • Author(s)
      中西敏浩・中村豪
    • Journal Title

      数学解析研究所講究録

      Volume: 1777 Pages: 62-74

    • Related Report
      2011 Annual Research Report
  • [Journal Article] A series associated to generating pairs of a once punctured torus group and a proof of McShane's identity2011

    • Author(s)
      中西敏浩
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 41 Pages: 11-25

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An application of Penner's coordinates of Teichmuller space of puncture surfaces, in Infinite dimensional Teichmuller spaces and moduli spaces2010

    • Author(s)
      中西敏浩
    • Journal Title

      RIMS Kokyuroku, Bessatsu

      Volume: Vol. B17 Pages: 105-114

    • NAID

      110007652294

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu-j.html

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] An application of Penner's coordinates of Teichmuller space of punctured surfaces2010

    • Author(s)
      Toshihiro Nakanishi
    • Journal Title

      RIMS Kokyuroku, Bessatsu

      Volume: B17 Pages: 105-114

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Parametrization of Teichmuller spaces by trace functions2012

    • Author(s)
      中西敏浩
    • Organizer
      Workshop on low dimensional conformalstructures and their groups
    • Place of Presentation
      University of Gdansk, Poland
    • Year and Date
      2012-06-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrization for Teichmuller spaces and its application to a representation of the mapping class groups2012

    • Author(s)
      中西敏浩
    • Organizer
      Rigidity School, Tokyo2011/2012
    • Place of Presentation
      東京大学大学院数理科学研究科(東京)
    • Year and Date
      2012-03-18
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrization for Teichmuller spaces and its application to a representation of the mapping class groups2012

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      Rigidity School, Tokyo 2011/2012
    • Place of Presentation
      東京大学大学院数理科学研究科(招待講演)
    • Year and Date
      2012-03-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] Parametrization of Teichmuller spaces by trace functions andits application2012

    • Author(s)
      中西敏浩
    • Organizer
      「リーマン面・不連続群論」研究集会
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科(名古屋)
    • Year and Date
      2012-01-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrization of Teichmuller space by trace functions and its applications2012

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      「リーマン面・不連続群論」研究集会
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科
    • Year and Date
      2012-01-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Trace parameters for Teichmuller spaces2011

    • Author(s)
      中村豪,中西敏浩
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      信州大学(長野)
    • Year and Date
      2011-09-30
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrization of Teichmuller spaces by trace functions2011

    • Author(s)
      中西敏浩
    • Organizer
      リーマン面に関する位相幾何学
    • Place of Presentation
      東京大学大学院理学研究科 (東京)
    • Year and Date
      2011-09-05
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrizations of Teichmuller spaces by trace functions2011

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-09-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Parametrization of Teichmuller spaces by trace functions2011

    • Author(s)
      中西敏浩
    • Organizer
      XVIth Conference on Analytic Functions and Related Topics
    • Place of Presentation
      PWSZ, Poland
    • Year and Date
      2011-06-27
    • Related Report
      2012 Final Research Report
  • [Presentation] Parametrization of Teichmuller spaces by trace functions2011

    • Author(s)
      中西敏浩
    • Organizer
      群の表現及び表現空間の幾何学的・解析的研究
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Year and Date
      2011-06-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Geodesic length parameters for Teichmuller space2011

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      Geometric and analytic approaches to representations of a group and representation spaces
    • Place of Presentation
      京都大学数学解析研究所
    • Year and Date
      2011-06-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] Penner's coordinate-system for a representation space of a punctured surface group and its applications, Geometry2010

    • Author(s)
      中西敏浩
    • Organizer
      Topology and Dynamics of Character Varieties
    • Place of Presentation
      National University of Singapore,Singapore
    • Year and Date
      2010-06-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Penner's coordinate-system for a representation space on a punctured surface group and its applications2010

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      Topology, Geometry and Dynamics of Character Varieties
    • Place of Presentation
      シンガポール国立大学
    • Year and Date
      2010-06-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Parametrization for Teichmuller spaces by trace functions

    • Author(s)
      Toshihiro Nakanishi
    • Organizer
      Workshop on low dimensional conformal structures and their groups, Gdansk ,Poland
    • Place of Presentation
      Gdansk, Poland
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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