Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cusped spaces and quasi-isometries of relatively hyperbolic groups   A group $\Gamma$ with a family of subgroups $\mathbb{P}$ is relatively
hyperbolic if $\Gamma$ admits a cusp-uniform action on a proper
$\delta$--hyperbolic space. We show that any two such spaces for a given group
pair are quasi-isometric, provided the spaces have "constant horospherical
distortion," a condition satisfied by Groves--Manning's cusped Cayley graph and
by all negatively curved symmetric spaces. Consequently the Bowditch boundary
admits a canonical quasisymmetric structure, which coincides with the
"naturally occurring" quasisymmetric structure of the symmetric space when
considering lattices in rank one symmetric spaces.
  We show that a group $\Gamma$ is a lattice in a negatively curved symmetric
space $X$ if and only if a cusped space for $\Gamma$ is quasi-isometric to the
symmetric space. We also prove an ideal triangle characterization of the
$\delta$--hyperbolic spaces with uniformly perfect boundary due to Meyer and
Bourdon--Kleiner. An appendix concerns the equivalence of several definitions
of conical limit point found in the literature.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph