Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic cones of HNN extensions and amalgamated products   Gromov asked whether an asymptotic cone of a finitely generated group was
always simply connected or had uncountable fundamental group. We prove that
Gromov's dichotomy holds for asympotic cones with cut points, as well as, HNN
extensions and amalgamated products where the associated subgroups are nicely
embedded. We also show a slightly weaker dichotomy for multiple HNN extensions
of free groups.

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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom