Geodesic
Some comments on piecewise-projective groups of the line
Nicolas Monod1 orcid
1École Polytechnique Fédérale de Lausanne, Switzerland
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 459-476

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DOI

We consider groups of piecewise-projective homeomorphisms of the line which are known to be non-amenable using notably the Carrière–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.
DOI : 10.4171/ggd/883
Classification : 43A07, 57M07
Mots-clés : fixed point, amenable group, von Neumann problem

Nicolas Monod  1

1 École Polytechnique Fédérale de Lausanne, Switzerland 
Nicolas Monod. Some comments on piecewise-projective groups of the line. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 459-476. doi: 10.4171/ggd/883
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