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2005 Fiscal Year Final Research Report Summary

Research on several geometry from the view point of sinuglarity theory

Research Project

Project/Area Number 15204002
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

IZUMIYA Shyuichi  Hokkaido Univ., Grad.school of Sci., Prof., 大学院・理学研究科, 教授 (80127422)

Co-Investigator(Kenkyū-buntansha) YAMAGUCHI Keizou  Hokkaido Univ., Grad.school of Sci., Prof., 大学院・理学研究科, 教授 (00113639)
ONO Kaoru  Hokkaido Univ., Grad.school of Sci., Prof., 大学院・理学研究科, 教授 (20204232)
ISHIKAWA Goo  Hokkaido Univ., Grad.school of Sci., Prof., 大学院・理学研究科, 教授 (50176161)
KANENOBU Taizou  Osaka city Univ., Grad.school of Sci., Prof., 大学院・理学研究科, 教授 (00152819)
MATSUMOTO Shigenori  Nihon Univ., Fac.of Sci.and Tech., Prof., 理工学部, 教授 (80060143)
Project Period (FY) 2003 – 2005
KeywordsSingularities / Topology / Differential Geometry / Dynamical System / Transformation group
Research Abstract

The purposes of the reasearch project were improvements of several areas in Topology and Differential Geometry which are roots of Singularity theory, constructions of new field for the applications of Singularity theory and developments of the applications of recent results of Singularity theory to Topology and Differential Geometry. For the purpose, we made a study on the following subjects and got many resutls : The higher order contact geomety, Symplectic Topology, Dynamical system and the theory of foliations, Knot theory, Topology on discrete groups, Topological dynamics and General Topology, geometric applications of Homotopical Algebra, groups of diffeomorphisms, Topological field theory and Riemannian geometry, Four dimensional topology.
I order to exchange the above researches, we organized the national conference on Topology on each year. We also organized several conferences on the above subjects. As researches on Singularity theory, we have studied Symplectic singularity theory, Global theory on singularities of smooth mappings, Fundamental group of algebraic curves and applications of singularity theory to Differential Geometry.
As a concequence, we established the puropose of the project. Especially, we organized the 12th MSJ-IRI International research institute "singularity theory and its applications" on September,2003 jointly with COE program of Hokkaido University "Nonlinear mathematics via singularities". We decided the puropose of the research project as the result of the conference. In the final year, we organized the special months "Singularity theory" (September,2005-12,2005) jointly with the above COE program. We confirmed the results of the project and the future problems in the speical months.

  • Research Products

    (14 results)

All 2005 2004 2003

All Journal Article (12 results) Book (2 results)

  • [Journal Article] The horospherical geometry of submanifolds in hyperbolic space2005

    • Author(s)
      S.IZUMIYA
    • Journal Title

      Journal of London Mathematical Society 71

      Pages: 779-800

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] h-vectors of Gorenstein^* simplicial posets2005

    • Author(s)
      M.Masuda
    • Journal Title

      Adv. Math. 194

      Pages: 332-344

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The horospsherical geometry of submanfiolds in hyperbolic space2005

    • Author(s)
      S.Izumiya
    • Journal Title

      J.of London Math.Soc. 71

      Pages: 779-800

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] h-vectors of Gorenstein* simplicial posets2005

    • Author(s)
      M.Masuda
    • Journal Title

      Adv.Math. 194

      Pages: 332-344

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Classifying singular Legendre curves by contactmorphism2004

    • Author(s)
      G.Ishikawa
    • Journal Title

      Journal of Geometry and Physics 52

      Pages: 113-126

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Supersingular K3 surfaces in odd characteristics and sextic double planes2004

    • Author(s)
      I.Shimada
    • Journal Title

      Math. Ann. 328

      Pages: 451-468

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On surjective Bing maps2004

    • Author(s)
      H.Kato
    • Journal Title

      Bull. Acad. Polon. Sci. Math. 52

      Pages: 329-333

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Classifying singular Legendrian curves by contactmorphisms2004

    • Author(s)
      G.Ishikawa
    • Journal Title

      J.of Geometry and Physics 52

      Pages: 113-126

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Super singular K3 surfaces in odd characteristics and sextic double planes2004

    • Author(s)
      I.Shimada
    • Journal Title

      Math.Ann. 328

      Pages: 451-468

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On surjective Bing maps2004

    • Author(s)
      H.Kato
    • Journal Title

      Bull.Acad.Polon.Sci.Math. 52

      Pages: 329-333

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Tangles with up to seven crossings2003

    • Author(s)
      T.Kanenobu
    • Journal Title

      Interdiscip. Inform. Sci 9

      Pages: 127-140

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Tangles with up to seven crossings.2003

    • Author(s)
      T.Kanenobu
    • Journal Title

      Interdiscrip.Inform.Sci. 9

      Pages: 127-140

    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] 切って、見て、触れてよくわかる「かたち」の数学2005

    • Author(s)
      泉屋周一
    • Total Pages
      133
    • Publisher
      日科技連出版
    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Cutting, Looking and Touching, Easy understanding "Mathematics of Shape" (In Japanese)2005

    • Author(s)
      S.Izumiya
    • Total Pages
      133
    • Publisher
      Nikka Giren Publ.
    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2007-12-13  

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