Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchically cocompact classifying spaces for mapping class groups of
  surfaces   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.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess