Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and non-existence of bounded packing in CAT(0) spaces and
  Gromov hyperbolic spaces   The main result of this paper is that given a group $G$ acting geometrically
by isometries on a CAT(0) space $X$ and a cyclic subgroup $H$ of $G$ generated
by a rank-1 isometry of $X$, $H$ has bounded packing in $G$. We give two proofs
of this result. The first one is by a characterization of rank-$1$ isometries
by Hamenstadt. The second proof follows directly from some results of
Dahmani-Guirardel-Osin and Sisto. Then using Mihailova's construction, we show
the existence of a finitely generated subgroup of the direct product of two
free groups $\mathbb F_2\times \mathbb F_2$ without the bounded packing
property answering a question of Hruska-Wise. We also prove the existence of
finitely presented subgroups of CAT(0) groups without bounded packing using
Wise's {\em modified Rip's construction} and the {\bf 1-2-3} theorem of
Baumslag, Bridson, Miller and Short.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph