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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On the finiteness of the classifying space for virtually cyclic subgroups

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