Smoothing countable group actions on metrizable spaces
Group Theory
2024-10-11 v2 Dynamical Systems
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.
Cite
@article{arxiv.2410.06077,
title = {Smoothing countable group actions on metrizable spaces},
author = {Inhyeok Choi and Sang-hyun Kim},
journal= {arXiv preprint arXiv:2410.06077},
year = {2024}
}
Comments
7 pages, to appear in the proceedings of the MSJ-SI