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arXiv · 2410.06077

Smoothing countable group actions on metrizable spaces

Inhyeok Choi·Sang-hyun Kim
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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. Hamenst\"{a}dt 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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Inhyeok Choi, Sang-hyun Kim. 2024-10-08. Smoothing countable group actions on metrizable spaces. https://arxiv.org/abs/2410.06077

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