Finite Mapping Class Group Orbits on Character Varieties

par Arnaud Maret (Université de Strasbourg)

lundi 7 avr. 2025, 14:00 → 15:15 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

The mapping class group of a surface is the group of isotopy classes of homeomorphisms of the surface. It acts on the space of conjugacy classes of morphisms from the fundamental group of the surface to some fixed Lie group. Such spaces are known as character varieties. In this talk we will investigate the rare phenomenon of finite orbits for mapping class group dynamics on character varieties. We will see how to construct non-trivial examples of finite orbits and give some intuition on how to classify all finite orbits when the target Lie group is SL(2,C). Most of this work is a collaboration with Samuel Bronstein.