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

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Puttkamer,  Timm von
Max Planck Institute for Mathematics, Max Planck Society;

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Wu,  Xiaolei
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/GGD/502
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Citation

Puttkamer, T. v., & Wu, X. (2019). On the finiteness of the classifying space for the family of virtually cyclic subgroups. Groups, Geometry, and Dynamics, 13(2), 707-729. doi:10.4171/GGD/502.


Cite as: https://hdl.handle.net/21.11116/0000-0004-725A-7
Abstract
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.