Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permanence properties of property A and coarse embeddability for locally
  compact groups   If $H$ is a lattice in a locally compact second countable group $G$, then we
show that $G$ has property A (respectively is coarsely embeddable into Hilbert
space) if and only if $H$ has property A (respectively is coarsely embeddable
into Hilbert space). Moreover, we show three interesting generalizations of
this result. If $H$ is a closed subgroup of $G$ that is co-amenable in $G$, and
if $H$ has property A (respectively, is coarsely embeddable into Hilbert
space), then we show that $G$ has property A (respectively, is coarsely
embeddable into Hilbert space). We also show that an extension of property A
groups still has property A. On the coarse embeddability side, we show that if
$\{e\}\rightarrow H\rightarrow G\rightarrow Q\rightarrow\{e\}$ is a short exact
sequence, and if either $H$ is coarsely embeddable into Hilbert space and $Q$
has property A, or $H$ is compact and $Q$ is coarsely embeddable into Hilbert
space, then $G$ is coarsely embeddable into Hilbert space. We extend the theory
of measure equivalence to locally compact non-unimodular groups. In a natural
way, we can also define measure equivalence subgroups. We show that property A
and uniform embeddability into Hilbert space pass to measure equivalence
subgroups. Using the same techniques, we show that also the Haagerup property,
weak amenability and the weak Haagerup property pass to measure equivalence
subgroups.

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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga