2001 Fiscal Year Final Research Report Summary
| Project/Area Number |
11640089
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Osaka Women's University |
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Principal Investigator |
IRIYE Kouyemon applied mathematics, Osaka Women's Universisity, Assistant Professor, 理学部, 助教授 (40151691)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIHARA Kazuo applied mathematics, Osaka Women's Universisity, Professor, 理学部, 教授 (90090563)
WATANABE Takashi applied mathematics, Osaka Women's Universisity, Professor, 理学部, 教授 (20089957)
WATANABE Yutaka applied mathematics, Osaka Women's Universisity, Professor, 理学部, 教授 (60028131)
YOSHITOMI Kentaro applied mathematics, Osaka Women's Universisity, Lecturer, 理学部, 講師 (10305609)
WATAMORI Yoko applied mathematics, Osaka Women's Universisity, Assistant Professor, 理学部, 助教授 (70240538)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Phantom maps / loop space / inverse limit / localigation |
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| Research Abstract |
In this reserach we studied phantom maps out of a single or iterated loop space Ω^kX of a simply connected finite complex X and related topics. We attacked the following problems raised by McGibbon in his survey paper.
(1) Let X be a simply connected finete complex which is not contractibel Is the universal phantom map out of the loop space Ω^κX essential?
(2) Does there exist a finite complex X and an essential phantom map from ΩX to a target of finite trpe?
(3) For a nilpotent group G we denot П_pG_(p) by G. Let {G_n} be an inverse sequence of finitely geneated nilpotent groups ans δ_* : lim__←^1G_n →lim__←^1G_n be the induced map between lim__←^1 sets. If lim__←^1G_n is nontrivial, does it follow that δ_*^-1(y) is an infinite set for each y in lim__←^1G_n?
As of the problem 1 we solved this problem except the case κ = 1. As of the problem 2 we obtained a negative answer when X is rationally elliptic or spaces are localized at a prime. As of problem 3 we obtained an affirmative answer.
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