Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of residually finite groups by isometries of the Urysohn
  space   As a consequence of Kirchberg's work, Connes' Embedding Conjecture is
equivalent to the property that every homomorphism of the group $F_\infty\times
F_\infty$ into the unitary group $U(\ell^2)$ with the strong topology is
pointwise approximated by homomorphisms with a precompact range. In this form,
the property (which we call Kirchberg's property) makes sense for an arbitrary
topological group. We establish the validity of the Kirchberg property for the
isometry group $Iso(U)$ of the universal Urysohn metric space $U$ as a
consequence of a stronger result: every representation of a residually finite
group by isometries of $U$ can be pointwise approximated by representations
with a finite range. This brings up the natural question of which other
concrete infinite-dimensional groups satisfy the Kirchberg property.

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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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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: cs
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex