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Geometry and topology of 3-manifolds II

Research Project

Project/Area Number 15204004
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTOKYO INSTITUTE OF TECHNOLOGY

Principal Investigator

KOJIMA Sadayoshi  Tokyo Institute of Technology, Mathematical and Computing Sciences, Professor, 大学院・情報理工学研究科, 教授 (90117705)

Co-Investigator(Kenkyū-buntansha) YOSHIDA Tomoyoshi  Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (60055324)
MORITA Shigeyuki  University of Tokyo, Department of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (70011674)
MATSUMOTO Shigenori  Nihon University, Department of Mathematics, Professor, 理工学部, 教授 (80060143)
SOMA Teruhiko  Tokyo Denki University, Department of Mathematical Sciences, Professor, 理工学部, 教授 (50154688)
OHTSUKI Tomotada  Kyoko University, Resaearch Institute of Mathematical Science, Associate professor, 数理解析研究所, 助教授 (50223871)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2005: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2004: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2003: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Keywordshyperboloic geometry / cone manifold / 3-dimensional topology / secondary characteristic class / lamination / foliation / geometric structure / volume / 錐多様体 / 双曲幾何学
Research Abstract

The purpose of this research project is to see the interaction of various geometric structures on 3-manifolds, to find principal idea behind them such as laws in physics and to promote the study of 3-manifolds interacting geometry and topology interdisciplinary. The current project based on the primary one that terminated on March 2003 was set up for 4 years and we have spent 3 years so far. Then we have decided to pre-renew the project by shifting the stress more on invariants because it seems to be necessary to do so in the light of recent progress on the current working subject. Fortunately, the new project was awarded as a continuing one and thus we here report our activity of the last 3 years.
In the last 3 years, we, the member of research group and collaborators, have promoted the project by doing research communication, organizing meetings and publishing research reports. As conclusion, we, the member of research group, have obtained a plenty of significant progress and simultaneously contributed the progress of this field. The research results were presented in the academic meetings including international ones. The details including one's by collaborators can be found in the attached report. In summary, according to the purpose of the project, we have darified what is needed for geometric methods to study topology of 3-manioflds more and more.
Looking at last 3 years, we must notice historical progress such as the solution of the ending lamination conjecture by Minsky-Brock-Canary the solution of Marden's conjecture by Agol and Calegari-Gabai and the approach to the geometrization by Hamilton and Perelman, which at least includes the solution of Poincare conjecture. Based on these, we set up the post geometrization by renewing our project with entitling "The geometry and invariants of 3-manifolds".

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (30 results)

All 2005 2004 2003 Other

All Journal Article (22 results) Book (1 results) Publications (7 results)

  • [Journal Article] Signatures of foliated surface bundles and the symplectomorphism groups of surfaces2005

    • Author(s)
      Kotschick, Morita
    • Journal Title

      Topology 44

      Pages: 131-149

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Ends of leaves of Lie foliations2005

    • Author(s)
      Hector, Matsumoto, Meigniez
    • Journal Title

      J. Math. Soc. of Japan 57

      Pages: 753-779

    • NAID

      10017177824

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Least area planes in Gromov hyperbolic space with co-compact metric2005

    • Author(s)
      T.Soma
    • Journal Title

      Geom. Dedicata 112

      Pages: 123-128

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Structures of foliated surface bundles and the Symplectomorphism groups of surfaces.2005

    • Author(s)
      D.Kotshick, S.Morita
    • Journal Title

      Topology 44

      Pages: 131-149

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Ends of leaves of Lie foliation.2005

    • Author(s)
      G.Hector, S.Matsumoto
    • Journal Title

      J.Math.Soc.of Japan 57

      Pages: 753-779

    • NAID

      10017177824

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Least area planes in Gromov hyperbolic space with co-compact metric2005

    • Author(s)
      T.Soma
    • Journal Title

      Geom.Dedicata 112

      Pages: 123-128

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Ends of leaves of Lie foliations2005

    • Author(s)
      Hector, Matsumoto, Meigniez
    • Journal Title

      J.Math.Soc.of Japan 57

      Pages: 753-779

    • NAID

      10017177824

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The Dehn filling space of a certain hyperbolic 3-orbifold2004

    • Author(s)
      Kojima, Mizushima
    • Journal Title

      Contemporary Math. 347

      Pages: 131-140

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Existence of least area planes in hyperbolic 3-space with co-compact metric2004

    • Author(s)
      T.Soma
    • Journal Title

      Topology 43

      Pages: 705-716

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Parabolic isometries of CAT(0) spaces and CAT(0) dimensions2004

    • Author(s)
      Fujiwara, Shioya, Yamagata
    • Journal Title

      Algebr.Geom.Topol. 4

      Pages: 861-892

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Generators for the tautological algebra of the moduli space of curves2003

    • Author(s)
      S.Morita
    • Journal Title

      Topology 42

      Pages: 787-819

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures and uniformization

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      Pacific J. Math (印刷中)(to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Circle packings on surfaces with projective structures : A survey

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      London Math. Soc., Lectures Notes (印刷中)(to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] An abelianization of SU(2) WZW model

    • Author(s)
      T.Yoshida
    • Journal Title

      To appear in Ann. of Math. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Circle packings on surfaces with projective structures and uniformization.

    • Author(s)
      S.Kojima, S.Mizushima, S.P.Tan
    • Journal Title

      Pacific J.Math. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Circle packings on surfaces with projective structures : A survey.

    • Author(s)
      S.Kojima, S.Mizushima, S.P.Tan
    • Journal Title

      London Math.Soc., Lecture Notes. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] An abelianization of SU(2) WZW model.

    • Author(s)
      T.Yoshida
    • Journal Title

      Ann.of Math. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Circle packings on surfaces with projective structures and uniformization

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      Pacific J.Math (To appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures : A survey

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      London Math.Soc., Lectures Notes (To appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] An abelianization of SU(2) WZW model

    • Author(s)
      T.Yoshida
    • Journal Title

      Ann.of Math. (To appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures and uniformization

    • Author(s)
      Kojima., Mizushima, Tan
    • Journal Title

      Pacific J.Math. (to appear)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Circle packings on surfaces with projective structures : A survey

    • Author(s)
      Kojima, Mizushima, Tan
    • Journal Title

      London Math.Soc., Lecture Notes (to appear)

    • Related Report
      2004 Annual Research Report
  • [Book] Affine flows on 3-manifolds2003

    • Author(s)
      S.Matsumoto
    • Total Pages
      94
    • Publisher
      American Mathematical Society
    • Related Report
      2004 Annual Research Report
  • [Publications] Kojima, Mizushima, Tan: "Circle packings on surfaces with projective structures"Journal of Differential Geometry. 63. 349-397 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kojima, Mizushima: "The Dehn filling space of a certain hyperbolic 3-orbifold"Contemporary Math.. (in-press)(to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] Yamashita, Nishi, Kojima: "Configuration spaces of points on the circle and hyperbolic Dehn fillings, II"Geometriae Dedicata. 89. 143-157 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Morita: "Generators for the tautological algebra of the moduli space of curves"Topology. 42. 787-819 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Matsumoto: "On the global rigidity of split Anosov R^n-actions"Journal of Mathematical Society of Japan. 55. 39-46 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Fujiwara: "Bounded cohomology of subgroups of mapping class groups"Geometry and Topology. 6. 69-89 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Matsumoto: "Affine flows on 3-manifolds"American Mathematical Society. 94 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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