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Amenability, Bilipschitz Maps, and the Von Neumann conjecture

Kevin Whyte
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Abstract

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups theory which show that the sign of the Euler characteristic is not a coarse invariant. Finally we get some general results on uniformly finite homology which we will apply to manifolds in a later paper.

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Kevin Whyte. 1997-04-05. Amenability, Bilipschitz Maps, and the Von Neumann conjecture. https://arxiv.org/abs/math/9704202

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