Classification of action of homeomorphisms on the fine curve graph of higher genus surfaces

by Nastaran Einabadi

Tuesday Nov 4, 2025, 11:15 AM → 12:15 PM Europe/Paris

1R2-207

In their 2022 work, Bowden, Hensel, and Webb 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. This connection has been established in the case of the 
torus leading to a complete classification. In this talk, I will present 
the progress that has been made towards solving the problem for higher 
genus surfaces.