# RELATIVELY AMENABLE ACTIONS OF THOMPSON’S GROUPS

@article{Scarparo2021RELATIVELYAA, title={RELATIVELY AMENABLE ACTIONS OF THOMPSON’S GROUPS}, author={Eduardo Scarparo}, journal={Bulletin of the Australian Mathematical Society}, year={2021} }

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.

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