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On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group

Frank Connolly·Benjamin Fehrman·Michael Hartglass
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Abstract

In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show that there exists no other model for the virtually-cyclic classifying space of G with dimension less than vcd(G)+1, where vcd(G) denotes the virtual cohomological dimension of G. In addition, the dimension of our construction realizes this limit.

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Frank Connolly, Benjamin Fehrman, Michael Hartglass. 2006-10-12. On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group. https://arxiv.org/abs/math/0610387

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