The Resolution Modules of A Space and Its Universal Covering Space

• 藤田 亮介

書誌事項

タイトル別名

• Resolution Modules of A Space and Its Universal Covering Space

抄録

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.

収録刊行物

• 岡山大学環境理工学部研究報告

  岡山大学環境理工学部研究報告 5 (1), 57-69, 2000-02-29

  岡山大学環境理工学部

キーワード

• G-CW-complex
• G-map
• G-poset

詳細情報

• CRID: 1390009224547657088
• NII論文ID: 40005123773
• NII論文ID: 120002313951
• NII書誌ID: AN10529213
• ISSN: 13419099
• DOI: 10.18926/fest/11566
• NDL書誌ID: 5633956
• Web Site: https://ousar.lib.okayama-u.ac.jp/11566
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I5633956
• 本文言語コード: ja
• データソース種別:
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  • IRDB
  • NDL
  • CiNii Articles