# 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.

## References

SHOWING 1-10 OF 17 REFERENCES

Boundary maps, germs and quasi-regular representations

- MathematicsAdvances in Mathematics
- 2022

We investigate the tracial and ideal structures of $C^*$-algebras of quasi-regular representations of stabilizers of boundary actions. Our main tool is the notion of boundary maps, namely…

C⁎-simplicity and representations of topological full groups of groupoids

- MathematicsJournal of Functional Analysis
- 2019

Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show…

Essential crossed products for inverse semigroup actions: simplicity and pure infiniteness

- Mathematics
- 2019

We define "essential" crossed products for inverse semigroup actions by Hilbert bimodules on C*-algebras and for Fell bundles over etale, locally compact groupoids. If the underlying groupoid is…

Topological full groups of ample groupoids with applications to graph algebras

- MathematicsInternational Journal of Mathematics
- 2019

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui’s definition of the topological full group from the compact to the locally compact case. We provide…

Cartan subalgebras and the UCT problem, II

- Mathematics
- 2015

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy…

Relative amenability

- Mathematics
- 2013

We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions,…

Topological amenability is a Borel property

- Mathematics
- 2013

We establish that a second countable locally compact groupoid possessing a continuous Haar system is topologically amenable if and only if it is Borel amenable. We give some examples and applications.

C*-Algebras and Finite-Dimensional Approximations

- Mathematics
- 2008

Fundamental facts Basic theory: Nuclear and exact $\textrm{C}^*$-algebras: Definitions, basic facts and examples Tensor products Constructions Exact groups and related topics Amenable traces and…

An invitation to bounded cohomology

- Mathematics
- 2006

A selection of aspects of the theory of bounded cohomology is presented. The emphasis
is on questions motivating the use of that theory as well as on some concrete issues suggested
by its study.…