The Burnside problem for locally compact groups

2018/12/31 by Thibaut Dumont, Dumont, Thibaut, Thibault Pillon +1
Mathematics · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1812.11743

Abstract

Using topological notions of translation-like actions introduced by Schneider, we give a positive answer to a geometric version of Burnside problem for locally compact group. The main theorem states that a locally compact group is non-compact if and only if it admits a translation-like action by the group of integers \mathbf Z. We then characterize the existence of cocompact translation-like actions of \mathbf Z or non-abelian free groups on a large class of locally compact groups, improving on Schneider's results and generalising Seward's.

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