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Topology of manifolds and geometric structures

Research Project

Project/Area Number 08454017
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

KONO Akira  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00093237)

Co-Investigator(Kenkyū-buntansha) KOKUBO Hiroshi  Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
NISHIDA Goro  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00027377)
MARUYAMA Masaki  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50025459)
UENO Kenji  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40011655)
FUKAYA Kenji  Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30165261)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥7,100,000 (Direct Cost: ¥7,100,000)
Fiscal Year 1997: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1996: ¥3,300,000 (Direct Cost: ¥3,300,000)
Keywordsinfinite dimensional Lie groups / free loop groups / gauge groups / moduli spaces / homoclinic orbits / 分類空間 / モ-スホモトピー / 量子化
Research Abstract

(1)Topology of infinite dimensional Lic groups
(2)Morse homotopy
Algebraic gcomctry and global analysis
Representation thcory and global analysis
(5)Dynamical systems
(1)A.Kono detcrmined the homotopy ring of free loop groups using the adjoint action of the groups on the based loop spaces. A.Kono also studied the problem of the relations between the isomorphic classcs of principal SU(2) bundles over a 1-counccted closcd 4-dimensional manifolds and the homotopy type of their classifying spaces and showed that the homotopy type of the classifying spaces almost detcrmined the isomorphic classcs of the bundles.
(2)K.Fukaya considered the family of Morsc functions on infinite dimensional spaces (e.g.moduli spaces)and defined sup products and cohomology operators using them.
(3)K.Ucno and Y.Shimizu considered problems on nonlincar differential cquations using algebraic geometry and obtained intercsting results on Kinizhink-Zamoldchikov cquations.
(4)M.Jimbo and T.Nomura obtained certain results on mathematical physics by using the methods of representation theory and quantum groups.
(5)H.lokubu studied various propertics on dynamical systems on manifolds and got results on homoclinic orbits.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] A.Kono: "A remark on the homotopy type of certain gauge groups" J.Math.Kyoto Univ.36. 115-121 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Hamanaka: "Adjoint actions on the modulo 5 homology groups of E_8 and ΩE_8" J.Math.Kyoto Univ.37. 169-176 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Fukaya: "Morse homotopy and Chem-Simons Perturbation theory" Commun.of Math.Phys.81. 37-90 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Fukaya: "Symplectic S-cobordism conjecture-summary-,Geometry and Physics" Lecture notes in pure and applied mathematics. 184. 209-220 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Ueno: "Neron-Severi groups for torus quasi bundles over curves,oduli of vector bundles" Lecture notes in pure and applied Math.179. 11-32 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 上野 健爾: "代数幾何1、岩波講座「現代数学の基礎」" 岩波書店, 177 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 上野 健爾: "代数幾何2、岩波講座「現代数学の基礎」" 岩波書店, 202 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Kono: "A remark on the homotopy type of certain gauge groups" J.Math.Kyoto Univ.36. 115-121 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Hamanaka: "Adjoint actions on the modulo 5 homology groups of E_8 and OMEGAE_8" J.Math.Kyoto Univ.37. 169-176 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Fukaya: "Morse homotopy and Dhem-Simons Perturbation theory" Commun.of Math.Phys.81. 37-90 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Fukaya: "Symplectic S-cobordism conjecturesummary-, Geometry and Physics" Lecture motes in pure andapplied mathematics. 184. 209-220 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Ueno: "Neron-Severi groups for torus quasi bundles over curves, oduli of vector bundles" Lecture notes in pure and applied Math. 179. 11-32 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Kono: "A remark on the homotopy type of certain gauge groups" J.Math.Kyoto Univ.36. 115-121 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Hamanaka: "Adjoint actions on the modulo 5 homology groups of E_8 and ΩE_8" J.Math.Kyoto Univ.37. 169-176 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Fukaya: "Morse homotopy and Chern-Simons Pertubation theory" Commun.of Math.Phys.81. 37-90 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Fukaya: "Symplectic S-cobordism conjecture-summary-,GEometry and Physics" Lecture notes in pure and applied mathematics. 184. 209-220 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Ueno: "Neron-Severi groups for torus quasi bundles over curves,oduli of vector bundles" Lecture notes in pure and applied Math.179. 11-32 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 上野 健爾: "代数幾何1、岩波講座「現代数学の基礎」" 岩波書店, 177 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 上野 健爾: "代数幾何2、岩波講座「現代数学の基礎」" 岩波書店, 202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.KONO S Tsukada: "a remark on the homotopy type of certain gange groups" J.Math.Kyoto Univ. 36. 115-121 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Hamanaka,S Hara A.KONO: "Adjoint actions of dio gronps on,the loop spaces and cohomology of exceptinal die groupe" Proc.of 1996 Korea-Japan conference on transfomation gronps. 43-49 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Hamanaka,S.Hara A.Kono: "Adjoint actions on the mod。lo5 homology groups of E_8 and ΩE_8" J.Math Kyoto Univ.37. (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Fukaya: "Morse homotopy and its guantization" AMS/IP Studies in Adv.Math.2. 409-440 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Fukaya: "Morse homotopy and Chen Simons Perturbation Theony" Conm.Math.Phisics. 181. 37-90 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M.Maruyama: "Construction of moduli space of stable sheaves via Simpson's idea" Proc.Taniguchi Sym.“Moduli and vector bomdles". 147-188 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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