Relatively amenable actions of Thompson's groups
Abstract
We investigate the notion of relatively amenable topological action and show that the action of Thompson's group $T$ on $S^1$ is relatively amenable with respect to Thompson's group $F$. We use this to conclude that $F$ is exact if and only if $T$ is exact. Moreover, we prove that the groupoid of germs of the action of $T$ on $S^1$ is Borel amenable.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- arXiv:
- arXiv:2109.01111
- Bibcode:
- 2021arXiv210901111S
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Operator Algebras
- E-Print:
- 6 pages. Minor change. Accepted in the Bulletin of the Australian Mathematical Society