Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Acylindrically hyperbolic groups and their quasi-isometrically embedded
  subgroups   We abstract the notion of an A/QI triple from a number of examples in
geometric group theory. Such a triple (G,X,H) consists of a group G acting on a
Gromov hyperbolic space X, acylindrically along a finitely generated subgroup H
which is quasi-isometrically embedded by the action. Examples include strongly
quasi-convex subgroups of relatively hyperbolic groups, convex cocompact
subgroups of mapping class groups, many known convex cocompact subgroups of
Out(Fn), and groups generated by powers of independent loxodromic WPD elements
of a group acting on a Gromov hyperbolic space. We initiate the study of
intersection and combination properties of A/QI triples. Under the additional
hypothesis that G is finitely generated, we use a method of Sisto to show that
H is stable. We apply theorems of Kapovich--Rafi and Dowdall--Taylor to analyze
the Gromov boundary of an associated cone-off. We close with some examples and
questions.

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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas