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1999 Fiscal Year Final Research Report Summary

Classifying spaces of Categories, Flore Homology and Homotopsy Theory of Infinite Complexes

Research Project

Project/Area Number 10440018
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  Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (00093237)

Co-Investigator(Kenkyū-buntansha) KOKUBU Hiroshi  Graduate School of Science, KYOTO UNIVERSITY, Associate Professor, 大学院・理学研究科, 助教授 (50202057)
FUKAYA Kenji  Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (30165261)
MARUYAMA Masaki  Graduate School of Science, KYOTO UNIVERSITY, Professor, 大学院・理学研究科, 教授 (50025459)
HAMANAKA Hiroaki  Faculty on Teacher Education, Hyogo Univ.of Education, Lecturer, 学校教育学部, 講師 (20294267)
NAKAJIMA Hiraku  Graduate School of Science, KYOTO UNIVERSITY, Associate Professor, 大学院・理学研究科, 助教授 (00201666)
Project Period (FY) 1998 – 1999
Keywordsgauge group / free loop group / adjoint representation / Hopf space / Conley homology / Flore homology / Classifying space
Research Abstract

The most important results of the research project are the following :
(1) Topology of infinite dimensional Lie groups
(2) Morse theory of infinite dimensional manifolds
(3) Classifying space of categories and dynamical systems
For (1) we determined homology ring of free loop groups for 1-connected Lie groups completely. Using the result we are nou determining the cohomology of the classifying spaces of them. For gauge groups, we showed the case when the base spaces are closed 1-connectedmanifolds and the structure group is SU(2), the homotopy type of the classifying spaces completely determine the boinotopy type of the base space and the isomorphism class of the bundles.
For (2) K. Fukaya solved the Anord conjecture using the Gromov-Witten iavariants.
For (3) we considered the Conley homology. We considerd a certain category and the cohomology of the classifying space of it is isomorphic to the Conley homology under some fine coditions.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] H. hamanaka: "Homotopy commutativity in spinor groups"J. Math. Kyoto Univ.. 40-2(掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A. Kono: "4-manifolds X over BSU(2) and the corresponding homotopy type"J. Pure and AppL. Algebra. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A. Kono: "Adjoint action of a finite loop space II"Proc. Roy. Soc. Edinburgh Sect. A. 129. 773-785 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Fukaya: "Arnold conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A. Moriwaki: "The continuity of Deligne pairing"internat. Math. Res. Notices. 1075-1066 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Hamanaka: "Homology ring mod 2 of free loop groups of spinor groups"J. Pure and AppL. Algebra. 146. 267-282 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Nakajima: "University Lecture Ser. Vol. 18, Lectures on Hilbert schemes of points on"AMS. 132 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Hmamanaka: "homotopy commutativity in spinor groups"J.Math.Kyoto Univ.. 40-2,(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Kono: "4-manifolds X over BSU(2) and the corresponding homotopy type Map(X,BSU(2))"J.Pure and AppL.Algebra. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Kono: "Adjoint action of a finite loop space II"Proc.Roy.Soc.Edinburgh Sect.A. 129. 773-785 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Fukaya: "Arnolod conjecture and Gromov-Witten invariant"Topology. 38. 933-1048 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Moriwaki: "The continuity of Deligne pairing"Internat.Math.Res.Notices. 1075-1066 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Hamanaka: "Homology ring mod 2 of free loopgroups of spinor groups"J.Pure and AppL.Algebra. 146. 267-282 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Nakajima: "Lectures on Hilbert schemes of points on surfaces"University Lecture Ser.. Vol.18 AMS. (1999)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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