Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms detecting stability and Morseness for finitely generated
  groups   The notions of stable and Morse subgroups of finitely generated groups
generalize the concept of a quasiconvex subgroup of a word-hyperbolic group.
For a word-hyperbolic group $G$, Kapovich provided a partial algorithm which,
on input a finite set $S$ of $G$, halts if $S$ generates a quasiconvex subgroup
of $G$ and runs forever otherwise. In this paper, we give various detection and
decidability algorithms for stability and Morseness of a finitely generated
subgroup of mapping class groups, right-angled Artin groups, toral relatively
hyperbolic groups, and finitely generated groups discriminated by a locally
quasiconvex torsion-free hyperbolic group (for example, ordinary limit groups).

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas