Towards geometric finiteness in mapping class groupsGeometric Group Theory Oberseminar

by Prof. Alessandro Sisto (Heriot-Watt University)

Wednesday Dec 17, 2025, 11:00 AM → 12:00 PM Europe/Berlin

Endenicher Allee 60/0-008 (Mathezentrum)

iven a subgroup of a mapping class group, there is a corresponding extension group, and fundamental groups of surface bundles (with injective monodromy) are exactly these extension groups.
Farb and Mosher introduced the notion of convex-cocompact subgroup of a mapping class group, and a subgroup is convex-cocompact if and only if the corresponding extension group is hyperbolic. Moving beyond this, one may wonder what happens for subgroups that are "close" to convex-cocompact. I will discuss some cases where the corresponding extension groups are hierarchically hyperbolic; I will explain what this means, what consequences this has, and speculate about notions of geometric finiteness in mapping class groups.
Based on joint works with Spencer Dowdall, Matt Durham, and Chris Leininger, and Jacob Russell.