1986 Fiscal Year Final Research Report Summary
Investigation of unstable homotopy theory
| Project/Area Number |
60540045
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Hyogo University of Teacher Education |
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Principal Investigator |
NOMURA Yasutoshi Hyogo University of Teacher Education, 学校教育学部, 教授 (20029630)
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| 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)
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| Project Period (FY) |
1985 – 1986
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| Keywords | Principal 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 |
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| 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.
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Research Products
(3 results)
