Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions

2010/05/07 by Martin Fluch, Fluch, Martin
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20F65 #msc:55R35

paper · pdf · doi:10.48550/arxiv.1005.1281

Improved construction in Section 4 which gives subsequently better estimates for the dimensions in Section 6. 15 pages

arxiv created 2010/07/03 · arxiv updated 2010/07/06

Abstract

Let G be an infinite cyclic extension, 1 -> B -> G -> Z -> 1, of a group B where the action of Z on the set of conjugacy classes of non-trivial elements of B is free. This class of groups includes certain ascending HNN-extensions with abelian or free base groups, certain wreath products by Z and the soluble Baumslag-Solitar groups BS(1,m) with |m|> 1. We construct a model for Evc(G), the classifying space of G for the family of virtually cyclic subgroups of G, and give bounds for the minimum dimension of Evc(G). We construct a 2-dimensional model for Evc(G) where G is a soluble Baumslag-Solitar BS(1,m) group with |m|>1 and we show that this model for Evc(G) is of minimal dimension.

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