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:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.01111
 Bibcode:
 2021arXiv210901111S
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Operator Algebras
 EPrint:
 6 pages. Minor change. Accepted in the Bulletin of the Australian Mathematical Society