Appears in collection : 2024 - T2 - WS1 - Low Dimensional Actions

The fine curve graph of a closed surface is a Gromov hyperbolic graph on which the group of homeomorphisms of the surface acts faithfully by isometry. In this mini-course, we will explore the links between the dynamics of a homeomorphism of the surface and the isometry type of its action on the fine curve graph. The first talk will be devoted to a dynamical characterization of homeomorphisms which act hyperbolically on the fine curve graph.

During the second talk, we will see examples of homeomorphisms which act parabolically on the fine curve graph and some results about them.

This is joint work with Jonathan Bowden, Sebastian Hensel, Kathryn Mann and Richard Webb for one aspect, and with Pierre-Antoine Guihéneuf for another.

Watch part 1