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Studies on Combinatorial Structures of 3-Manifolds

Research Project

Project/Area Number 10640089
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ISHII Ippei  Keio Univ., Dept.of Math., Associate Prof., 理工学部, 助教授 (90051929)

Co-Investigator(Kenkyū-buntansha) OHTA Katsuhiro  Keio Univ., Dept.of Math., Associate Prof., 理工学部, 助教授 (40213722)
ENOMOTO Hikoe  Keio Univ., Dept.of Math., Prof., 理工学部, 教授 (00011669)
MAEDA Yoshiaki  Keio Univ., Dept.of Math., Prof., 理工学部, 教授 (40101076)
KOUNO Masaharu  Kitami Inst.of Tech., Dept.of Information, Prof., 教授 (40170203)
IKEDA Hiroshi  Keio Univ., Dept.of Math., Prof., 理学部, 教授 (10031353)
森吉 仁志  慶應義塾大学, 理工学部, 助教授 (00239708)
松本 眞  慶應義塾大学, 理工学部, 助教授 (70231602)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords3-manifold / spine / Heegaard splitting / Dehn surgery / Poincare conjecture / 三次元多様体 / ヘゴール分解 / Heegaard分解 / framed link / Dehn手術 / spine / DS-deagram
Research Abstract

(1) On Ds-diagrams
It was shown that two Ds-diagrams representing the same closed 3-manifold can be transformed to each other by a sequence of "elementary deformations".
(2) On Heegaard splittings
A new condition for a Heegaard splitting to be reducible has been found. This condition is described by the notion of a "d-pseudo core".
(3) On framed links in a homotopy 3-sphere
It was shown that any homotopy 3-sphere admits a "very special framed link" , which enjoys a good property and closely related to a Heegaard splitting.
(4) On the Poincare conjecture
Using the above two results (2) and (3), we have proposed a new method for attacking the famous "Poincare conjecture".

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] H. Enomoto: "A Lower Bound for the Edge-Crossings over the Spine of the Book embedding of Graphs"Discrete Applied Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Enomoto: "Connecte Sabgraphs with Small Subgraphs with Small Degree sums in 3-connected Plane Graphs"J. Graph Theory. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Omori: "Noncommutable 2-sphere"J. Math. Soc. Japan. 50. 915-943 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Ikeda: "Remodeling a DS-diagram into one with E-cycle"Tokyo J. Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Ishii: "A new condition for a Heegaard spliffine to be reductable"Tokyo J. Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Ihsii: "Very special framed links for a homotopy 3-sphere"Tokyo J. Math. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Enomoto, M.S. Miyauchi and K. Ota: "A lower Bound for the number of Edge-Crossings over the Spine of the Book Embeding of Graphs"Discrete Applied Mathematics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Enomoto and K. Ota: "Connected Subgraphs with Small Subgraphs with Small Degree Sums in 3-Connected Planar Graphs"Journal of Graph Theory. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kozono, Y. Maeda and H. Naito: "A Yang-Mills-Higgs gradient flow on RィイD13ィエD1 blowing up at infinity"Proc. Japan Acad. 74 Ser. A, No.5. 71-73 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Omori, Y. Maeda, N. Miyazaki and A. Yoshioka: "Noncommutative 3-sphere; A model of noncommutative contact algebras"J. Math. Soc. Japan. 50. 915-943 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Ikeda, M. Yamashita and K. Yokoyama: "Remodeling a DS-diagram into one with E-cycle"Tpkyp J. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Ishii: "A new condition for a Heegaard splitting to be reducible"(preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Ishii: "Very special framed links for a homotopy 3-sphere"(preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Enomoto: "A Lower Bound for the Edge-Crossings over the Spine of the Book Erbeddig of Graphs"Discrofe Applied Math.. (to appesr).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Enomoto: "Connecte Subgraphs with Small Subgrophs with Small Degres Su*s in 3-connected planer Graphs"J.Groph Theory. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Omori: "Noncommutative 3-sphere"J.Math.Soc.Japan. 50. 915-943 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.Ikeda: "Remodeling a DS-diagram into one with E-cycle"Tokyo J.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Ishii: "A new condition for a Heegaard splitting to be reducible"Tokyo J.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Ishii: "Very special framed links for a homotopy 3-sphere"Tokyo J.Math.. (to appear).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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