Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gromov boundaries as Markov compacta   We prove that the Gromov boundary of every hyperbolic group is homeomorphic
to some Markov compactum. Our reasoning is based on constructing a sequence of
covers of $\partial G$, which is quasi-$G$-invariant wrt. the ball $N$-type
(defined by Cannon) for $N$ sufficiently large. We also ensure certain
additional properties for the inverse system representing $\partial G$, leading
to a finite description which defines it uniquely.
  By defining a natural metric on the inverse limit $\lim K_n$ and proving it
to be bi-Lipschitz equivalent to an accordingly chosen visual metric on
$\partial G$, we prove that our construction enables providing a simplicial
description of the natural quasi-conformal structure on $\partial G$. We also
point out that the initial system of covers can be modified so that all the
simplexes in the resulting inverse system are of dimension less than or equal
to $\dim \partial G$.
  We also generalize --- from the torsion-free case to all finitely generated
hyperbolic groups --- a theorem guaranteeing the existence of a finite
representation of $\partial G$ of another kind, namely a semi-Markovian
structure (which can be understood as an analogue of the well-known automatic
structure of $G$ itself).

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg