Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-isometries need not induce homeomorphisms of contracting
  boundaries with the Gromov product topology   We consider a `contracting boundary' of a proper geodesic metric space
consisting of equivalence classes of geodesic rays that behave like geodesics
in a hyperbolic space. We topologize this set via the Gromov product, in
analogy to the topology of the boundary of a hyperbolic space. We show that
when the space is not hyperbolic, quasi-isometries do not necessarily give
homeomorphisms of this boundary. Continuity can fail even when the spaces are
required to be CAT(0). We show this by constructing an explicit example.

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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg