On the classifying space of the family of virtually cyclic subgroups

Details On the classifying space of the family of virtually cyclic subgroups On the classifying space of the family of virtually cyclic subgroups

2007-02-22

arxiv.org/abs/math/0702646v2

Mathematics

Algebraic Topology

Final version, to appear in the Proceedings in honour of Farrel and Jones in Pure and Applied Mathematic Quarterly. 45 pages

Scientific paper

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually cyclic. We give examples of groups for which the difference of the minimal dimensions of the classifying spaces of virtually cyclic and of finite subgroups is -1, 0 and 1, and show in many cases that no other values can occur.

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