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arXiv · 1712.00496

Hierarchically cocompact classifying spaces for mapping class groups of surfaces

Brita Nucinkis·Nansen Petrosyan
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Abstract

We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group $\mbox{Mod}(S)$ of any connected oriented compact surface $S$, possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most $\mbox{vcd} \mbox{Mod}(S)+1$. When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of L\"{u}ck for mapping class groups of surfaces.

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Brita Nucinkis, Nansen Petrosyan. 2017-12-01. Hierarchically cocompact classifying spaces for mapping class groups of surfaces. https://doi.org/10.1112/blms.12166

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