NDLI: Free and properly discontinuous actions of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1*_{G_0}G

Content Provider	Paperity
Author	Gonçalves, Daciberg Lima Golasiński, Marek
Abstract	We estimate the number of homotopy types of orbit spaces for all free and properly discontinuous cellular actions of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1_{G_0}G_2\). In particular, homotopy types of orbits of \((2n-1)\)-spheres \(\Sigma (2n-1)\) for such actions are analysed, provided the groups \(G_0, G_1, G_2\) and G are finite and periodic. This family of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1_{G_0}G_2\) contains properly the family of virtually cyclic groups. The possible actions of those groups on the top cohomology of the homotopy sphere are determined as well.
Starting Page	803
Ending Page	824
File Format	HTM / HTML
ISSN	21938407
DOI	10.1007/s40062-016-0158-7
Issue Number	4
Journal	Journal of Homotopy and Related Structures
Volume Number	11
e-ISSN	15122891
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-12-01
Access Restriction	Open
Subject Keyword	57s17 Primary 20e36 Secondary 20f28 Periodic group Homotopy sphere Virtually cyclic group 55m35 Orbit space Free and properly discontinuous cellular action
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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Free and properly discontinuous actions of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1*_{G_0}G_2\)