Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonpositively curved 2-complexes with isolated flats   We introduce the class of nonpositively curved 2-complexes with the Isolated
Flats Property. These 2-complexes are, in a sense, hyperbolic relative to their
flats. More precisely, we show that several important properties of
Gromov-hyperbolic spaces hold `relative to flats' in nonpositively curved
2-complexes with the Isolated Flats Property.
  We introduce the Relatively Thin Triangle Property, which states roughly that
the fat part of a geodesic triangle lies near a single flat. We also introduce
the Relative Fellow Traveller Property, which states that pairs of
quasigeodesics with common endpoints fellow travel relative to flats, in a
suitable sense. The main result of this paper states that in the setting of
CAT(0) 2-complexes, the Isolated Flats Property is equivalent to the Relatively
Thin Triangle Property and is also equivalent to the Relative Fellow Traveller
Property.

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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat