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arXiv · 1101.0951

Uniform Embeddability into Hilbert Space

A. Khukhro
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Abstract

The open question of what prevents a metric space with bounded geometry from being uniformly embeddable in Hilbert space is answered here for box spaces of residually finite groups. We prove that a box space does not contain a uniformly embedded expander sequence if and only if it uniformly embeds in Hilbert space. In particular, this gives a sufficient condition for a residually finite group to have the Haagerup property. The main result holds in the more general setting of a disjoint union of Cayley graphs of finite groups with bounded degree.

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A. Khukhro. 2011-03-29. Uniform Embeddability into Hilbert Space. https://arxiv.org/abs/1101.0951

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