Some comments on piecewise-projective groups of the line
Group Theory
2023-05-02 v1 Dynamical Systems
Operator Algebras
Abstract
We consider groups of piecewise-projective homeomorphisms of the line which are known to be non-amenable using notably the Carriere--Ghys theorem on ergodic equivalence relations. Replacing that theorem by an explicit fixed-point argument, we can strengthen the conclusion and exhibit uncountably many "amenability gaps" between various piecewise-projective groups.
Cite
@article{arxiv.2305.00796,
title = {Some comments on piecewise-projective groups of the line},
author = {Nicolas Monod},
journal= {arXiv preprint arXiv:2305.00796},
year = {2023}
}