Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite asymptotic dimension for CAT(0) cube complexes   In this paper we prove that the asymptotic dimension of a finite-dimensional
CAT(0) cube complex is bounded above by the dimension. To achieve this we prove
a controlled colouring theorem for the complex. We also show that every CAT(0)
cube complex is a contractive retraction of an infinite dimensional cube. As an
example of the dimension theorem we obtain bounds on the asymptotic dimension
of small cancellation groups.

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat