About von Neumann's problem for locally compact groups
arXiv:1702.07955 · doi:10.4171/JNCG/317
Abstract
We note a generalization of Whyte's geometric solution to the von Neumann problem for locally compact groups in terms of Borel and clopen piecewise translations. This strengthens a result of Paterson on the existence of Borel paradoxical decompositions for non-amenable locally compact groups. Along the way, we study the connection between some geometric properties of coarse spaces and certain algebraic characteristics of their wobbling groups.
14 pages, no figures