# On the finiteness of the classifying space for the family of virtually cyclic subgroups

@article{Puttkamer2016OnTF, title={On the finiteness of the classifying space for the family of virtually cyclic subgroups}, author={Timm von Puttkamer and Xiaolei Wu}, journal={Groups, Geometry, and Dynamics}, year={2016} }

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups.

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