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Description
Quid of action of homeomorphisms on the fine curve graph
We can associate to a surface its fine curve graph, which is a Gromov hyperbolic space. The homeomorphisms of the surface act as isometries on the fine curve graph, either hyperbolically, parabolically, or elliptically. It turns out that the problem of classifying homeomorphisms based on the type of their action on this graph, is related to the rotational behaviour of homeomorphisms. In this talk, I will present these notions, and the question of classification. Then, I will present some of the work that has already been done to solve this problem.
