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

Timm von Puttkamer; Xiaolei Wu

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arXiv · 1607.03790

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

Timm von Puttkamer·Xiaolei Wu

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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.

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Timm von Puttkamer, Xiaolei Wu. 2016-07-13. On the finiteness of the classifying space for the family of virtually cyclic subgroups. https://arxiv.org/abs/1607.03790

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