岡山大学環境理工学部研究報告 ISSN 2187-6940
Published by Faculty of Environmental Science and Technology, Okayama University

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The Resolution Modules of A Space and Its Universal Covering Space

Fujita, Ryousuke
Abstract
Let G be a finite group, Y a finite connected G-CW-complex, and let Ⅱ(Y) denote G-poset (in the sense of Oliver-Petrie) associated to Y. They defined the abelian group Ω(G,Ⅱ(Y)) consisting of all equivalent classes of Ⅱ(Y)-complexes. They also defined the subgroup Φ(G,Ⅱ(Y)) related to Ⅱ(Y)-resolutions. We call Φ(G,Ⅱ(Y)) the resolution module of Y. Applying the Oliver-Petrie theory to the universal covering space Y, we obtain the group Ω(G,Ⅱ(Y)), where G is a certain extension of G by π(1)(Y). Then the canonical homomorphism ν : Ω(G,Ⅱ(Y))→ Ω(G,Ⅱ(Y)) induced by the projection Y → Y is an isomorphism. In this paper, for G = Z(p)×Z(q) we construct a finite G-CW-complex Y such that π(1)(Y) Zq and ν(Φ(G,Ⅱ(Y)) ≠ Φ(G,Ⅱ(Y)), where p and q are arbitrary distinct primes.
Keywords
G-CW-complex
G-map
G-poset
ISSN
1341-9099
NCID
AN10529213