Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-ended subgroups of graphs of free groups with cyclic edge groups   Consider a one-ended word-hyperbolic group. If it is the fundamental group of
a graph of free groups with cyclic edge groups then either it is the
fundamental group of a surface or it contains a finitely generated one-ended
subgroup of infinite index. As a corollary, the same holds for limit groups. We
also obtain a characterisation of surfaces with boundary among free groups
equipped with peripheral structures.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci