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Synthetic Studies ofTopology

Research Project

Project/Area Number 17204007
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNihon University

Principal Investigator

MATSUMOTO Shigenori  Nihon University, Collge of Science and Technology, Professor (80060143)

Co-Investigator(Kenkyū-buntansha) TSUBOI Takashi  the University of Tokyo, Graduate School of Mathematical Science, Professor (40114566)
OHSHIKA Ken'ichi  Ohsaka University, Graduate School of Science, Professor (70183225)
KOHNO Akira  Kyoto University, Graduate School of Science, Professor (00093237)
小島 定吉  東京工業大学, 大学院・情報理工学研究科, 教授 (90117705)
IZUMIYA Shuichi  Hokkaido University, Graduate School of Science, Professor (80127422)
FUKAYA Kenji  Kyoto Univeisity, Graduate School of Science, Professor
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥45,500,000 (Direct Cost: ¥35,000,000、Indirect Cost: ¥10,500,000)
Fiscal Year 2007: ¥18,590,000 (Direct Cost: ¥14,300,000、Indirect Cost: ¥4,290,000)
Fiscal Year 2006: ¥18,590,000 (Direct Cost: ¥14,300,000、Indirect Cost: ¥4,290,000)
Fiscal Year 2005: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Keywordsmanifold / roun action / dynamical systems / manning class group / hyperbolic space / homotopv group / singularity / foliation / 写像類群 / 結び目
Research Abstract

Recent progress of topology is prompted by the recognition of its relationship with the other area of mathematics which includes differential Geometry, algebra, analysis and mathematical physics. This makes the method of investigation more sophisticated and gives the researches wider perspectives. The purpose of this research project is to make cooperation of various researchers easy and timingly, making the field more active .
We have successfully maintained the network of topologists, organized various symposia and conferences timingly, did exchanges of the researchers, invited various well recognized foreign researchers, gave many colloquia abroad, thus contributing to the development of topology in a significant way.
Concretely the research of the following areas of topology is developed by our research projects: Theory of singularities of algebraic and differentiable maps: Group actions on manifolds and on simplicial complexes: Actions of mapping class groups on Teichmuller spaces of the surface: Theory of dynamical systems of complex analytic maps: Dynamical study of vector fields on manifolds and foliation theory: Geometirc study of hyperbolic 3-manifold: Differential structure of 4-manifolds and symplectic structures: Conformal field theory: Homotopy theory: Invariants of knots and links: General topology especially those concerned with wild spaces.
In Japan, topology is developing constantly by the efforts of many researchers, and it gained worldwide recognition.
Grant in aid by the Japan Society for the Promotion of Science is indispensable in this development. We express our hearty gratitude to the JSPS.

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (25 results)

All 2007 2006 2005

All Journal Article (21 results) (of which Peer Reviewed: 6 results) Presentation (3 results) Book (1 results)

  • [Journal Article] Spacelike parallels and Legendrian singularities2007

    • Author(s)
      Shuichi Izumiya, Masatomo Takahashi
    • Journal Title

      Journal of Geometry and Physics 57

      Pages: 3789-3803

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Torus graphs and simplicial posets2007

    • Author(s)
      Hirshi Maeda, Mikiya Masuda, Taras Panov
    • Journal Title

      Advances in Mathematics 212

      Pages: 711-746

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Singular fibers and characteristic classes2007

    • Author(s)
      Osamu Saeki, Takahiro Yamamoto
    • Journal Title

      Topology and Applications 155

      Pages: 112-120

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] "Spacelike parallels and Legendrian singularities" with referee2007

    • Author(s)
      Shuichi, Izumiya, Masatomo, Takahashi
    • Journal Title

      Journal of Geometry and Physics with referee Vol. 57

      Pages: 3789-3803

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Torus graphs and simplicial posets2007

    • Author(s)
      Hiroshi, Maeda, Mikiya, Masuda, TAras, Panov
    • Journal Title

      Advances in Mathematics with referee Vol. 212

      Pages: 711-746

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Singular fibers and characteristic classes2007

    • Author(s)
      Osamu, Saeki, Takahiro, Yamamoto
    • Journal Title

      Topology and Application, with referee Vol. 155

      Pages: 112-120

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Spacelike parallels and Legendrian singularities2007

    • Author(s)
      Shuichi Izumiya and Masatomo Takahashi
    • Journal Title

      Journal of Geometry and Physics 57

      Pages: 3789-3803

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Torus graphs and simplicial posets2007

    • Author(s)
      Hiroshi Maeda, Mikiya Masuda and Taras Panov
    • Journal Title

      Advances in Mathematics 212

      Pages: 711-746

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular fibers and characteristic classes2007

    • Author(s)
      Osamu Saeki and Takahiro Yamamoto
    • Journal Title

      Topology and Applications 155

      Pages: 112-120

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The horospherical Gauss-Bonnet type theorem in hyperbolic space2006

    • Author(s)
      S.Izumiiya, M.C.Romero-Fuster
    • Journal Title

      J. Math. Soc.Japan 58.4

      Pages: 965-984

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Tr. Mat. Inst. Steklova 2522006

    • Author(s)
      Cohomology of open torus manifolds
    • Journal Title

      Geom. Topol.,Diskret. Geom. i Teor. Mnozh.

      Pages: 158-166

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The first four terms of Kauffman's link polynomial.2006

    • Author(s)
      Kanenobu, Taizo
    • Journal Title

      Kyungpook Mathematical Journal 46.4

      Pages: 509-525

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Cobordism of Morse functions on surfaces, universal complex of singular fibers, and their application to map germs2006

    • Author(s)
      0.Saeki
    • Journal Title

      Algebraic and Geometric Topology 6

      Pages: 539-572

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Circle Packings on Surfaces with Projective Structures and Uniformization,2006

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

      Pacific J. Math., 225

      Pages: 287-300

    • Related Report
      2006 Annual Research Report
  • [Journal Article] lqlq{0n the group of foliation preserving diffeomorphisms}lqlq,Foliations 2005, Lodz2006

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      World Scientific, Singapore

      Pages: 411-430

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Ends of Leaves of Lie foliations2005

    • Author(s)
      Matsumoto, Shigenori et al.
    • Journal Title

      J. Math. Soc, Japan 57・3

      Pages: 753-779

    • NAID

      10017177824

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Different links with the same Links-Gould invariant2005

    • Author(s)
      Kanenobu, Taizo et al.
    • Journal Title

      Osaka J. Math. 42・2

      Pages: 273-290

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Group generated by half transvections2005

    • Author(s)
      Tsuboi, Takashi
    • Journal Title

      Kodai Math. J. 28

      Pages: 463-482

    • NAID

      130003574505

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Generic smooth maps with sphere fibers2005

    • Author(s)
      Saeki, Osamu et al.
    • Journal Title

      J. Math. Soc. Japan 57・3

      Pages: 881-902

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Signatures of foliated surface bundles and the symplectomorphism groups of surfaces2005

    • Author(s)
      Morita, Shigeyuki et al.
    • Journal Title

      Topology 44

      Pages: 131-149

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The horospherical geometry of submanifolds in Hyperbolic space2005

    • Author(s)
      Izumiya, Shuichi et al.
    • Journal Title

      Journal of London Mathematical Society 71

      Pages: 779-800

    • Related Report
      2005 Annual Research Report
  • [Presentation] Parameter rigid flows on 3-manifolds2007

    • Author(s)
      Shigenori Matsumoto
    • Organizer
      Troisieme Colloque Maghrebin de Geonmetrie, Topologie et Systemes Dynamiques
    • Place of Presentation
      Marrakech,Marroco
    • Year and Date
      2007-06-01
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Parameter rigid flows on 3-manifolds2007

    • Author(s)
      Shigenori, Matsumoto
    • Organizer
      Troisieme Colloque Maghrebin de Geometrie, Topologie et Systemes Dyaniniqus
    • Place of Presentation
      Marrakech, Marroco
    • Year and Date
      2007-06-01
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Parameter rigid flows on 3-manifolds2007

    • Author(s)
      Shigenori Matsumoto
    • Organizer
      Troisieme Colloque Maghrebin de Geometrie, Topologie et Systemes Dynamiques
    • Place of Presentation
      Marrakech, Marroco
    • Year and Date
      2007-06-01
    • Related Report
      2007 Annual Research Report
  • [Book] Kleinian groups which are limits of geometrically finite groups2005

    • Author(s)
      Ohshika, Ken'ichi
    • Publisher
      Amer. Math. Soc.
    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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