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Manifolds with Actions of Cyclic Groups

Research Project

Project/Area Number 10640068
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionYokohama National University

Principal Investigator

KITADA Yasuhiko  Yokohama Nat. Univ., Fac. Eng., Prof., 工学部, 教授 (70016145)

Co-Investigator(Kenkyū-buntansha) HIRANO Norimichi  Yokohama Nat. Univ., Grad. School Eng., Prof., 工学研究科, 教授 (80134815)
TAMANO Kenichi  Yokohama Nat. Univ., Fac. Eng., Prof., 工学部, 教授 (90171892)
TERADA Toshiji  Yokohama Nat. Univ., Grad. School Eng., Prof., 工学研究科, 教授 (80126383)
NISHIMURA Takashi  Yokohama Nat. Univ., Fac. Edu. Hum. Sci., Ass. Prof., 教育人間科学部, 助教授 (80189307)
NAGURA Maki  Yokohama Nat. Univ., Fac. Eng., Assis., 工学部, 助手 (40251772)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordstransformation group / surgery / characteristic class / Kervaire class / Steenrod algebra / 手術理論 / Kervaire不変量
Research Abstract

The project team made researches concerning the relation between Kervaire classes in different dimensions in order to utilize the result to obtain informations on surgery obstructions on the quotient manifold with finite cyclic group actions.
1. In May 1999, we announced the newly discovered relation of Kervaire clases :
SqィイD12a+1ィエD1SqィイD12aィエD1SqィイD12a-1ィエD1KィイD22a-2ィエD2 + (SqィイD12a+1ィエD1SqィイD12a-1ィエD1 + SqィイD12a+2a-1ィエD1SqィイD12aィエD1)KィイD22a+1-2ィエD2 = 0
In July 1999, we announced the result concerning smooth Kervaire classes at Topology Conference at Morelia (Mexico) :
A(a, b, c) : SqィイD12bィエD1SqィイD12cィエD1KィイD22a+1-2ィエD2 + SqィイD12a+1ィエD1SqィイD12bィエD1SqィイD12cィエD1KィイD22a-2ィエD2 = O(a > b > c 【greater than or equal】 0)
The paper is submitted to "Topology and its Applications".
3. By symbolic calculation method of computers up to dimension 200, we obtained a conjecture stronger than the one stated in item 1 :
B(a, b) : SqィイD12a+1ィエD1SqィイD12aィエD1SqィイD12bィエD1KィイD22a-2ィエD2 + (SqィイD12a+1ィエD1SqィイD12bィエD1 + ΣィイD4b-1ィエD4ィイD5i=1ィエD5 SqィイD12a+1-2iィエD1SqィイD12b+2iィエD1SqィイD12b+2iィエD1) KィイD22a+1-2ィエD2 = 0 (a > b > 0)
4. The relations A(a, b, c) and B(a, b) account for all the additive 45 relations of Kervaire classes over the mod 2 Steenrod algebra up to dimension 200. We have already made preliminary preparations for B(a, b) and its proof will soon be completed.

Report

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

    (20 results)

All Other

All Publications (20 results)

  • [Publications] T. Terada: "Topological C_k(X) and C_p(X) : Embeddings and isomorphisms"Tsukuba 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] K. Tamano: "Definitions of Signa-space"Topology proceedings. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] X. Feng and K. Tamano: "Countably fan-tight subspaces of countable product of Laznev spaces are metrizable"Topology proceedings. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Hirano: "Existence of entire solutions for semilinear elliptic problems on R^N"Iopol, Methods Nonlinear Analysis. 13. 1-15 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Terada: "Order-preserving homeomorphisums between spaces of continuous functions"General Topology Symposium(Kochi Univ.). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Nishimura: "Isomorphisms of smooth map germs with isomorphic local algebras"Pitman Research Notes in Math Series. 381. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Terada: "Topological CィイD2kィエD2(X) and CィイD2pィエD2(X) : Embeddings and isomorphisms"Tsukuba J. Math.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Tamano: "Definitions of Sigma-spaces"Topology Proceedings. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] X. Feng and K. Tamano: "Country fan-tight subspaces of countable product of Lasnev spaces are metrizable"Topology Proceedings. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Hirano: "Existence of entire solutions for semilinear elliptic problems on RィイD1NィエD1"Topol. Methods Nonlinear Anal.. vol. 13. 1-15 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Terada: "Order-preserving homeomorphisms between spaces of continuous functions"General Topology Symposium at Kochi Univ.. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Sakai, K. Tamano and Y. Yajima: "Regular networks for metrizable spaces and Lasnev spaces"Bull. Polish Acad. Sci. Math.. vol. 46. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Nishimura: "Isomorphisms of smooth map germs with isomorphic local algebras"Pitman Research Notes in Math Series. vol. 381. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiji Terada: "Topological lattices C_k(X) and Cp(X) : Embeddings and Isomorphisms"Tsukuba J. Math. (in press).

    • Related Report
      1999 Annual Research Report
  • [Publications] Norimichi Hirano: "Existence of entire solutions for semilinear elliptic problems on R^N"Topol. Methods Nonlinear Anal.. 13(1). 1-15 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Terada: "Order-preserving homeomorphisms between spaces of real-valued continuous functions" General,Topology Symposium at Kochi University. 23-28 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Sakai,K.Tamano,and Y.Yajima: "Regular networks for metrizable spaces and Lasnev spaces" Bull.Polish Acad.Sci.Math.46. 121-133 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] X.Feng and K.Tamano: "Countably fan-tight subspaces of a countable product of Lasnev spaces are metrizable" to appear in “Topology Proceedings".

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Tamano: "Definitions of Sigma-spaces" to appear in “Topology Proceedings".

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Nishimura: "Isomorphisms of smooth map germs with isomorphic local algebras" Pltman Research Notes in Mathematical Series. 381. 94-106 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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