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Riemann surfaces and low dimensional manifolds

Research Project

Project/Area Number 26400095
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionGakushuin University

Principal Investigator

Matsumoto Yukio  学習院大学, 理学部, 研究員 (20011637)

Co-Investigator(Renkei-kenkyūsha) Ashikaga Tadashi  東北学院大学, 工学部, 教授 (90125203)
Komori Yohei  早稲田大学, 教育総合科学学術院, 教授 (70264794)
Ohmoto Toru  北海道大学, 理学研究科, 教授 (20264400)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsリーマン面 / ドリーニュ・マンフォードコンパクト化 / オービフォールド / 結晶群 / 4次元多様体 / タイヒミュラー空間 / モジュライ空間 / カーブ複体 / 写像類群 / コンパクト化
Outline of Final Research Achievements

It is known that the moduli space of Riemann surfaces admits a natural compactification called the Deligne-Mumford compactification (DM-compactification). The main result of the present research is that we explicitly constructed a "natural" atlas consisting of orbifold charts on the DM-compactification of moduli space. These charts are indexed by the simplices of Harvey's curve complex. As a byproduct of the result, we discovered that certain higher dimensional euclidean crystallographic groups are attached to those orbifold charts that are indexed by the simplices of the maximum dimension. The theoretical meaning of this attachment of crystallographic groups will be studied in the future.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (18 results)

All 2018 2017 2016 2015 2014

All Presentation (18 results) (of which Int'l Joint Research: 3 results,  Invited: 17 results)

  • [Presentation] Orbifold charts of the compactified moduli spaces and crystallographic groups2018

    • Author(s)
      松本幸夫
    • Organizer
      リーマン面・不連続群研究集会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 4次元多様体とLefschetzファイバー空間2017

    • Author(s)
      松本幸夫
    • Organizer
      第64回トポロジーシンポジューム
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Compactification of moduli spaces and crystallographic groups2016

    • Author(s)
      Yukio Matsumoto
    • Organizer
      Workshop on Grothendieck-Teichmuller Theories
    • Place of Presentation
      Nankai University, Tianjin, China
    • Year and Date
      2016-07-25
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] リーマン面のモジュライ空間と結晶群2016

    • Author(s)
      松本幸夫
    • Organizer
      第8回早稲田大学 数学・応用数学談話会
    • Place of Presentation
      早稲田大学 西早稲田キャンパス63号館
    • Year and Date
      2016-06-30
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Moduli spaces and crystallographic groups2016

    • Author(s)
      Yukio Matsumoto
    • Organizer
      Two lectures at Fudan University
    • Place of Presentation
      Fudan University, Shanghai, China
    • Year and Date
      2016-06-01
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Riemann surfaces and crystallographic groups2016

    • Author(s)
      Yukio Matsumoto
    • Organizer
      International workshop on low-dimensional topology
    • Place of Presentation
      Dalian University of Technology, Dalian, China
    • Year and Date
      2016-05-06
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Riemann surfaces and crystallographic groups2016

    • Author(s)
      Yukio Matsumoto
    • Organizer
      Colloquim Talk
    • Place of Presentation
      University of South Florida, USA
    • Year and Date
      2016-04-22
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] モジュライ空間のコンパクト化と結晶群2016

    • Author(s)
      松本幸夫
    • Organizer
      2016年日本数学会年会、特別講演
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Riemann surfaces and Crystallographic Groups2016

    • Author(s)
      Yukio Matsumoto
    • Organizer
      2016 Winter TAPU Workshop on Knots and Related Topics
    • Place of Presentation
      College of Natural Sciences, Kyungpook National University, Daegu, Korea
    • Year and Date
      2016-02-16
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Crystallographic groups arising from Teichmuller spaces2015

    • Author(s)
      Yukio Matsumoto
    • Organizer
      Master-Class, Finsler geometry and applications to low-dimensional geometry and topology and moduli spaces
    • Place of Presentation
      Palazzo delle Scienze, Cagliari-Sardinia, Italy
    • Year and Date
      2015-09-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] モジュライ空間、カーブ複体、結晶群2015

    • Author(s)
      松本幸夫
    • Organizer
      研究集会「リーマン面に関連する位相幾何学」
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2015-08-27
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Curve complexes and the DM-compactification of moduli spaces of Riemann surfaces2015

    • Author(s)
      Yukio Matsumoto
    • Organizer
      RIMS Seminar "Topology, Geometry and Algebra of low dimensional manifolds"
    • Place of Presentation
      KKR Numazu Hamayu
    • Year and Date
      2015-05-29
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Curve complexes and the DM-compactification of moduli spaces2015

    • Author(s)
      松本幸夫
    • Organizer
      Branched coverings, Degenerations and Related Topics
    • Place of Presentation
      東北学院大学、多賀城キャンパス
    • Year and Date
      2015-02-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Relatively non-singular hermitian forms in low and higher dimensional knot theory2015

    • Author(s)
      Yukio Matsumoto (松本幸夫)
    • Organizer
      the 10th East Asian School of Knots and Related Topics
    • Place of Presentation
      華東師範大学、上海
    • Year and Date
      2015-01-26
    • Related Report
      2014 Research-status Report
  • [Presentation] Ivanovの「切り詰めタイヒミュラー空間」とモジュライ空間のコンパクト化について2014

    • Author(s)
      松本幸夫
    • Organizer
      研究集会「多様体のトポロジーの展望」
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2014-11-29
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Teichmuller spaces as infinite polyhedra2014

    • Author(s)
      Yukio Matsumoto (松本幸夫)
    • Organizer
      Summer School-Finsler geometry with applications
    • Place of Presentation
      Univ. the Aegean, Greece
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Teichmuller spaces as infinite polyhedra2014

    • Author(s)
      Yukio Matsumoto (松本幸夫)
    • Organizer
      FJV2014-Sapporo (The 2nd Franco-Japanese-Vietnames Sympo.)
    • Place of Presentation
      北海道大学、理学部
    • Year and Date
      2014-08-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Four dimensional manifolds and Riemann surfaces (2 lectures)2014

    • Author(s)
      Yukio Matsumoto (松本幸夫)
    • Organizer
      Fudan University, Geometry seminar
    • Place of Presentation
      復旦大学、上海
    • Year and Date
      2014-05-13 – 2014-05-16
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2019-03-29  

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