1. Test for amenability for extensions of infinite residually finite groups
- Author
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Cortez, María Isabel and Gómez, Jaime
- Subjects
Mathematics - Dynamical Systems ,Mathematics - Group Theory ,37B05, 37B10, 20E26 - Abstract
Let $G$ be a countable group that admits a minimal equicontinuous action on the Cantor set (for example, a residually finite group). We show that the family of almost automorphic actions of $G$ on the Cantor set, is a test for amenability for $G$. More precisely, we show that if $G$ is non-amenable, then for every minimal equicontinuous system $(Y, G)$, such that $Y$ is a Cantor set, there exists a Toeplitz subshift with no invariant probability measures, whose maximal equicontinuous factor is $(Y,G)$. Consequently, we obtain that $G$ is amenable if and only if every Toeplitz $G$-subshift has at least one invariant probability measure., Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:2312.12562
- Published
- 2024