Smoothing countable group actions on metrizable spaces

2024/10/08 by Choi, Inhyeok, Kim, Sang-hyun
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.06077

Abstract

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenstädt regarding finitely generated groups, and our proof is based upon her idea. This also gives a simple proof of a theorem due to Deroin, Kleptsyn and Navas regarding one-manifolds. We also establish an analogous result for closed subgroups of locally compact groups.

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