Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-isometric rigidity for graphs of virtually free groups with
  two-ended edge groups   We study the quasi-isometric rigidity of a large family of finitely generated
groups that split as graphs of groups with virtually free vertex groups and
two-ended edge groups. Let $G$ be a group that is one-ended, hyperbolic
relative to virtually abelian subgroups, and has JSJ decomposition over
two-ended subgroups containing only virtually free vertex groups that aren't
quadratically hanging. Our main result is that any group quasi-isometric to $G$
is abstractly commensurable to $G$. In particular, our result applies to
certain "generic" HNN extensions of a free group over cyclic subgroups.

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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: cs