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arXiv · 1111.0569

Box spaces, group extensions and coarse embeddings into Hilbert space

A. Khukhro
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Abstract

We investigate how coarse embeddability of box spaces into Hilbert space behaves under group extensions. In particular, we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated residually finite amenable group has a box space which coarsely embeds into Hilbert space. This provides a new class of examples of metric spaces with bounded geometry which coarsely embed into Hilbert space but do not have property A, generalising the example of Arzhantseva, Guentner and Spakula.

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A. Khukhro. 2011-11-02. Box spaces, group extensions and coarse embeddings into Hilbert space. https://arxiv.org/abs/1111.0569

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