Commensurators and classifying spaces with virtually cyclic stabilizers

Details Commensurators and classifying spaces with virtually cyclic stabilizers Commensurators and classifying spaces with virtually cyclic stabilizers

2011-08-31

arxiv.org/abs/1108.6279v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

By examining commensurators of virtually cyclic groups, we show that for each natural number n, any locally finite-by-virtually cyclic group of cardinality aleph_n admits a finite dimensional classifying space with virtually cyclic stabilizers of dimension n+3. As a corollary, we prove that every elementary amenable group of finite Hirsch length and cardinality aleph_n admits a finite dimensional classifying space with virtually cyclic stabilizers.

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