Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions

Details Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions

2010-05-07

arxiv.org/abs/1005.1281v2

Mathematics

Group Theory

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

Scientific paper

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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