On non-amenable embeddable spaces in relation with free products
K\'evin Boucher
TL;DR
This paper establishes conditions under which free products of residually finite groups have embeddable box spaces, creating new non-amenable metric spaces that coarsely embed into Hilbert space, extending previous constructions.
Contribution
It generalizes prior work by providing sufficient conditions for embeddability of box spaces in free products, introducing a new class of non-amenable spaces with bounded geometry.
Findings
Free products of residually finite groups can have embeddable box spaces under certain conditions.
Constructs a new class of non-amenable metric spaces with bounded geometry.
These spaces coarsely embed into Hilbert space.
Abstract
In this paper we give sufficient conditions for a free product of residually finite groups to admit an embeddable box space. This generalizes the constructions of Arzhantseva, Guentner and Spakula in arXiv:1101.1993v2 and gives a new class of non-amenable metric spaces with bounded geometry which coarsely embeds into Hilbert space.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Geometric and Algebraic Topology · Holomorphic and Operator Theory