Handlebody group of genus two as an HHG
Marissa Miller (UIUC)
Abstract: The handlebody group is the mapping class group of a handlebody. In this talk, I will show that the handlebody group of genus two is a hierarchically hyperbolic group (HHG). As a consequence, I will show that the stable subgroups of the genus two handlebody group are those subgroups whose orbit maps are quasi-isometric embeddings into the disk graph, (a characterization which does not hold for higher genus handlebody groups). This is analogous to a characterization of stable subgroups of surface mapping class groups.