Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embeddability of generalized wreath products and box spaces   Given two finitely generated groups that coarsely embed into a Hilbert space,
it is known that their wreath product also embeds coarsely into a Hilbert
space. We introduce a wreath product construction for general metric spaces
X,Y,Z and derive a condition, called the (delta-polynomial) path lifting
property, such that coarse embeddability of X,Y and Z implies coarse
embeddability of X\wr_Z Y. We also give bounds on the compression of X\wr_Z Y
in terms of delta and the compressions of X,Y and Z. Next, we investigate the
stability of the property of admitting a box space which coarsely embeds into a
Hilbert space under the taking of wreath products. We show that if an infinite
finitely generated residually finite group H has a coarsely embeddable box
space, then G\wr H has a coarsely embeddable box space if G is finitely
generated abelian. This leads, in particular, to new examples of bounded
geometry coarsely embeddable metric spaces without property A.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an