Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Commensurability invariance for abelian splittings of right-angled Artin
  groups, braid groups and loop braid groups
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th