Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cohomology rings of tree braid groups   Let $\Gamma$ be a finite connected graph. The (unlabelled) configuration
space $UC^n \Gamma$ of $n$ points on $\Gamma$ is the space of $n$-element
subsets of $\Gamma$. The $n$-strand braid group of $\Gamma$, denoted
$B_n\Gamma$, is the fundamental group of $UC^n \Gamma$.
  We use the methods and results of our paper "Discrete Morse theory and graph
braid groups" to get a partial description of the cohomology rings $H^*(B_n
T)$, where $T$ is a tree. Our results are then used to prove that $B_n T$ is a
right-angled Artin group if and only if $T$ is linear or $n<4$. This gives a
large number of counterexamples to Ghrist's conjecture that braid groups of
planar graphs are right-angled Artin groups.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph