Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cross ratios and cubulations of hyperbolic groups   Many geometric structures associated to surface groups can be encoded in
terms of invariant cross ratios on their circle at infinity; examples include
points of Teichm\"uller space, Hitchin representations and geodesic currents.
We add to this picture by studying cubulations of arbitrary Gromov hyperbolic
groups $G$. Under weak assumptions, we show that the space of cubulations of
$G$ naturally injects into the space of $G$-invariant cross ratios on the
Gromov boundary $\partial_{\infty}G$.
  A consequence of our results is that essential, hyperplane-essential
cubulations of hyperbolic groups are length-spectrum rigid, i.e. they are fully
determined by their length function. This is the optimal length-spectrum
rigidity result for cubulations of hyperbolic groups, as we demonstrate with
some examples. In the hyperbolic setting, this constitutes a strong improvement
on our previous work in arXiv:1903.02447.
  Along the way, we describe the relationship between the Roller boundary of a
${\rm CAT(0)}$ cube complex, its Gromov boundary and - in the non-hyperbolic
case - the contracting boundary of Charney and Sultan.
  All our results hold for cube complexes with variable edge lengths.

34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph