Finite rigid sets and the separating curve complex

For each closed surface of genus $gge3$, we find a finite subcomplex of the separating curve complex that is rigid with respect to incidence-preserving maps.

Convex-cocompact subgroups of the Goeritz group

We show that finitely-generated, purely pseudo-Anosov subgroups of the genus-2 Goeritz group are convex cocompact in the genus-2 mapping class group.