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Investigation of unstable homotopy theory

Research Project

Project/Area Number 60540045
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionHyogo University of Teacher Education

Principal Investigator

NOMURA Yasutoshi  Hyogo University of Teacher Education, 学校教育学部, 教授 (20029630)

Co-Investigator(Kenkyū-buntansha) MATSUYAMA Hiroshi  Hyogo University of Teacher Education, 学校教育学部, 助教授 (80028266)
KOIKE Satoshi  Hyogo University of Teacher Education, 学校教育学部, 助教授 (60161832)
WATANABE Kinji  Hyogo University of Teacher Education, 学校教育学部, 助教授 (20004468)
ITAGAKI Yoshio  Hyogo University of Teacher Education, 学校教育学部, 教授 (30006431)
YANAGIHARA Hiroshi  Hyogo University of Teacher Education, 学校教育学部, 教授 (00033803)
Project Period (FY) 1985 – 1986
Project Status Completed (Fiscal Year 1986)
Budget Amount *help
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1986: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1985: ¥700,000 (Direct Cost: ¥700,000)
KeywordsPrincipal fibration / Category / <M_k> -map / <N_k> -space / Homotopy fibre / Pushout / Phantom map / 双対性 / 左ホモトピー逆 / ファントム写像
Research Abstract

We have defined the notion of <M_k> -map as a generalization of a homotopy monomorphism introduced by P. J. Hilton and studied by T. Ganea. Let a principal fibration call an <M_(infinte)> -map if it is an <M_k> -map for every positive integer k. No principal fibration has not been known which is an <M_(infinte)> -map but admits no left homotopy inverse. In this research we have succeeded to construct such examples, using phantom maps in complex K-theory.
The notion of homotopy pullbacks and pushouts is important in developing unstable homotopy theory. In this investigation we introduce the notion of a triad and cotriad of squares and interprete a theorem of Mather-Walker concerning commutativity of homotopy limits and colimits, which allows us to extend their result. Further we can obtain some approximation theorems to the duals of preceding theorems.

Report

(1 results)
  • 1986 Final Research Report Summary
  • Research Products

    (3 results)

All Other

All Publications (3 results)

  • [Publications] 野村泰敏: Hyogo University of Teacher Education Journal. 7. (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Yasutoshi NOMURA: " <M_(infinite)> -maps having no left homotopy inverse" Hyogo University of Education Journal. 7. 1-2 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary
  • [Publications] Yasutoshi NOMURA: "On homotopy limits and colimits"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1986 Final Research Report Summary

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Published: 1987-03-31   Modified: 2016-04-21  

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