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math.DS2023
Hyperbolic isometries of the fine curve graph of higher genus surfaces
Pierre-Antoine Guihéneuf, Emmanuel Militon
We prove that for a homeomorphism f that is isotopic to the identity on a closed hyperbolic surface, the following are equivalent: * f acts hyperbolically on the fine curve graph;…
math.DS2023
Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative
Dominique Malicet, Emmanuel Militon
In 2000, Margulis proved that any group of homeomorphisms of the circle either preserves a probabilty measure on the circle or contains a free subgroup in two generators, which is…
math.DS2023
Parabolic isometries of the fine curve graph of the torus
Pierre-Antoine Guiheneuf, Emmanuel Militon
In this article we finish the classification of actions of torus homeomorphisms on the fine curve graph initiated by Bowden, Hensel, Mann, Militon, and Webb in \cite{BHMMW}. This i…