Spherical space forms--Homotopy types and self-equivalences for the groups \(\mathbb Z/a \rtimes \mathbb Z/b\) and \(\mathbb Z/a \rtimes(\mathbb Z/b \times \mathbb Q_{2^i})\)
type: Item
instance of: scholarly article
title: Spherical space forms--Homotopy types and self-equivalences for the groups \(\mathbb Z/a \rtimes \mathbb Z/b\) and \(\mathbb Z/a \rtimes(\mathbb Z/b \times \mathbb Q_{2^i})\)
zbMATH Open document ID: 1068.55001
author: Marek Golasiński
author: Daciberg Lima Gonçalves
published in: Topology and its Applications
publication date: 2005-02-22T00:00:00Z
review text: If \(\gamma: G\times X\to X\) is a free and celluar action, where \(X\) is a CW complex homotopy equivalent to a sphere, then the quotient \(X/\gamma\) is called a spherical space form. Two spherical space forms \(X/\gamma\) and \(X'/\gamma\) are said to be equivalent if they are homeomorphic; they are homotopic (denoted \(\simeq\)) if they are homotopy equivalent. The set of equivalence classes of spherical space forms \(X/\gamma\) where \(X\simeq S^{2d-1}\) is denoted \(\mathcal{K}_G^{2d-1}\). The first main result of this paper determines the cardinality of the set \(\mathcal{K}_G^{2d-1}/\simeq\) for groups of the form described in the title, and for certain dimensions \(2d-1\); the statement is too technical to be stated here. The second main result, also very technical, describes the group of self-equivalences of spherical space forms.
reviewed by: Jeffrey Strom
Mathematics Subject Classification ID: 55M35
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 2136483
zbMATH Keywords: automorphism group
zbMATH Keywords: CW-complex
zbMATH Keywords: spherical space form
zbMATH Keywords: free and cellular G-action
zbMATH Keywords: group of self homotopy equivalences
MaRDI profile type: Publication
full work available at URL: j.topol.2003.08.030
OpenAlex ID: W2060286925
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DOI: 10.1016/J.TOPOL.2003.08.030
description: scientific article; zbMATH DE number 2136483