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New development of the theory of infinite dimensional Teichmuller spaces: construction of moduli spaces

Research Project

Project/Area Number 23740102
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionChiba University

Principal Investigator

FUJIKAWA Ege  千葉大学, 理学(系)研究科(研究院), 准教授 (80433788)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords複素解析学 / リーマン面 / 擬等角写像 / タイヒミュラー空間 / 写像類群 / モジュライ空間 / 双曲幾何学 / 擬等角写像類群 / タイヒミュラーモジュラー群 / タイヒミュラー空間論
Research Abstract

On the classification of the Teichmuller modular transformations in infinite dimensional Teichmuller spaces, we investigated properties of transformations of infinite discrete type and those of divergent type. We also observed asymptotic Teichmuller modular transformations acting on asymptotic Teichmuller spaces and obtained a sufficient condition to be of finite order. Furthermore, for a subgroup of the quasiconformal mapping class group that is stationary, we observed discontinuity of the action on the space of asymptotically conformal classes.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (23 results)

All 2014 2013 2012 2011 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (12 results) (of which Invited: 1 results) Remarks (1 results)

  • [Journal Article] Topological characterization of the asymptotically trivial mapping class group2014

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Handbook of Group Actions (Higher Education Press and International Press)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Coherence of limit points in the fibers over the asymptotic Teichmuller space2014

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Computational Methods and Function Theory

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topological characterization of the asymptotically trivial mapping class group2014

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Handbook of Group Actions, Higher Education Press and International Press

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of asymptotic Teichmuller modular transformation2013

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Contemporary Mathematics

      Volume: 590 Pages: 40-50

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-divergent infinitely discrete Teichmuller modular transformation2013

    • Author(s)
      Ege Fujikawa and Katsuhiko Matsuzaki
    • Journal Title

      Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (Tohoku University Press)

      Pages: 97-102

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Nielsen realization problem for asymptotic Teichmuller modular groups2013

    • Author(s)
      Ege Fujikawa and Katsuhiko Matsuzaki
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 365 Pages: 3309-3327

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non-divergent infinitely discrete Teichmuller modular transformation2013

    • Author(s)
      Ege Fujikawa and Katsuhiko Matsuzaki
    • Journal Title

      Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

      Volume: なし

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Discontinuity of asymptotic Teichmuller modular group2012

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, Contemporary Mathematics

      Volume: 575 Pages: 77-88

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Discontinuity of asymptotic Teichmuller modular group2012

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Contemporary Mathematics

      Volume: 575

    • Related Report
      2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Nielsen realization problem for asymptotic Teichmuller modular groups2012

    • Author(s)
      Ege Fujikawa and Katsuhiko Matsuzaki
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 掲載確定済

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Coherence of limit points in the fiber over the asymptotic Teichmuller space2013

    • Author(s)
      Ege Fujikawa
    • Organizer
      the 21st International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Nanjing University, China
    • Year and Date
      2013-06-17
    • Related Report
      2013 Final Research Report
  • [Presentation] The order of periodic elements of the asymptotic Teichmuller modular group2013

    • Author(s)
      Ege Fujikawa
    • 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
      2013-01-12
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Peripheral quasiconformal automorphism groups and the Nielsen realization problem2012

    • Author(s)
      藤川英華
    • Organizer
      複素力学系の新展開
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-12-12
    • Related Report
      2013 Final Research Report
  • [Presentation] Fixed point theorems in infinite dimensional Teichmuller spaces2012

    • Author(s)
      Ege Fujikawa
    • Organizer
      Low-dimensional Geometry and Topology
    • Place of Presentation
      Tokyo Institute of Technology
    • Year and Date
      2012-09-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Periodicity of asymptotic Teichmuller modular transformations2012

    • Author(s)
      Ege Fujikawa
    • Organizer
      Group Actions and Applications in Geometry, Topology and Analysis
    • Place of Presentation
      Kunming University of Science and Technology, Yunnan, China
    • Year and Date
      2012-07-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Periodicity of asymptotic Teichmuller modular transformations2011

    • Author(s)
      Ege Fujikawa
    • Organizer
      the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Aster Plaza, Hiroshima
    • Year and Date
      2011-12-12
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Topological characterization of the asymptotically trivial mapping class group2011

    • Author(s)
      Ege Fujikawa
    • Organizer
      International Conference on Analysis, In Memory of Professor Sheng Gong
    • Place of Presentation
      Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
    • Year and Date
      2011-08-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Topological characterization of the asymptotically trivial mapping class group2011

    • Author(s)
      Ege Fujikawa
    • Organizer
      International Conference on Analysis, In Memory of Professor Sheng Gong(招待講演)
    • Place of Presentation
      Chinese Academy of Sciences
    • Related Report
      2011 Research-status Report
  • [Presentation] Coherence of limit points in the fiber over the asymptotic Teichmuller space

    • Author(s)
      Ege Fujikawa
    • Organizer
      The 21st International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Nanjing University, China
    • Related Report
      2013 Annual Research Report
  • [Presentation] Periodicity of asymptotic Teichmuller modular transformations

    • Author(s)
      Ege Fujikawa
    • Organizer
      Group actions and applications in geometry, topology and analysis
    • Place of Presentation
      Kunming University of Science and Technology, China
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Fixed point theorems in infinite dimensional Teichmuller spaces

    • Author(s)
      Ege Fujikawa
    • Organizer
      Low-dimensional Geometry and Topology
    • Place of Presentation
      東京工業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Peripheral quasiconformal automorphism groups and the Nielsen realization problem

    • Author(s)
      Ege Fujikawa
    • Organizer
      複素力学系の新展開
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www.math.s.chiba-u.ac.jp/~fujikawa/

    • Related Report
      2013 Final Research Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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