Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Acylindrical hyperbolicity of groups acting on quasi-median graphs and
  equations in graph products   In this paper we study group actions on quasi-median graphs, or 'CAT(0) prism
complexes', generalising the notion of CAT(0) cube complexes. We consider
hyperplanes in a quasi-median graph $X$ and define the contact graph
$\mathcal{C}X$ for these hyperplanes. We show that $\mathcal{C}X$ is always
quasi-isometric to a tree, generalising a result of Hagen, and that under
certain conditions a group action $G \curvearrowright X$ induces an
acylindrical action $G \curvearrowright \mathcal{C}X$, giving a quasi-median
analogue of a result of Behrstock, Hagen and Sisto.
  As an application, we exhibit an acylindrical action of a graph product on a
quasi-tree, generalising results of Kim and Koberda for right-angled Artin
groups. We show that for many graph products $G$, the action we exhibit is the
'largest' acylindrical action of $G$ on a hyperbolic metric space. We use this
to show that the graph products of equationally noetherian groups over finite
graphs of girth $\geq 6$ are equationally noetherian, generalising a result of
Sela.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin