Monod, Nicolas2025-08-202025-08-202025-08-19202510.4171/GGD/8832-s2.0-105012831357https://infoscience.epfl.ch/handle/20.500.14299/253035We 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.falseamenable groupfixed pointvon Neumann problemtext::journal::journal article::research article