Homotopy types of orbit spaces and their self-equivalences for the periodic groups Z/a \rtimes (Z/b x T^⋆_n) and Z/a \rtimes (Z/b x O^⋆_n)

2006/02/21 by Marek Golasinski, Marek Golasiński, Golasinski, Marek +3
Mathematics · #20F28 #55M35 #55P15 (Primary) 20E22 #57S17 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20E22 #msc:20F28 #msc:55M35 #msc:55P15 #msc:57S17

paper · pdf · doi:10.48550/arxiv.math/0602452

21 pages

arxiv created 2006/02/21 · openalex publication_date 2006/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group given in one of the forms listed in the title with period 2d and X(n) an n-dimensional CW-complex with the homotopy type of an n-sphere. We study the automorphism group Aut(G) to compute the number of distinct homotopy types of orbit spaces X(2dn-1)/μwith respect to free and cellular G-actions μon all CW-complexes X(2dn-1). At the end, the groups E(X(2dn-1)/μ) of self homotopy equivalences of orbit spaces X(2dn-1)/μassociated with free and cellular G-actions μon X(2dn-1) are determined.

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