Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of one-relator groups satisfying a polynomial isoperimetric
  inequality   For every pair of positive integers $p > q$ we construct a one-relator group
$R_{p,q}$ whose Dehn function is $\simeq n^{2 \alpha}$ where $\alpha =
\log_2(2p / q)$. The group $R_{p,q}$ has no subgroup isomorphic to a
Baumslag-Solitar group $BS(m,n)$ with $m \neq \pm n$, but is not automatic, not
CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a
long-standing question on the automaticity of one-relator groups and gives
counterexamples to a conjecture of Wise.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con