Box spaces, group extensions and coarse embeddings into Hilbert space

Details Box spaces, group extensions and coarse embeddings into Hilbert space Box spaces, group extensions and coarse embeddings into Hilbert space

2011-11-02

arxiv.org/abs/1111.0569v2

Mathematics

Group Theory

Updated references, the term "uniform" replaced by "coarse", 15 pages

Scientific paper

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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