Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thickness of $\mathsf{Out}(A_1*...*A_n)$   In this paper we have examined hyperbolicity and relative hyperbolicity of
$\Gamma_n := \mathsf{Out}(G_n)$ , where $G_n = A_1*...*A_n$, is a finite free
product and each $A_i$ is a finite group. We have used the $\mathsf{Out}(G_n)$
action on the Guirardel-Levitt deformation space, to find a virtual generating
set and prove quasi isometric embedding of a large class of subgroups. We have
used ideas from works of Mosher-Handel and Alibegovi\'c to prove
non-distortion. We have used these subgroups to prove that $\Gamma_n$ is thick
for higher complexities. Thickness was developed by Behrstock-Dru\c{t}u-Mosher
and thickness implies that the groups are non-relatively hyperbolic.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs