Abstract: Studying the distortion properties of naturally occuring subgroups of the mapping class group plays an important part in understanding its large-scale geometry. In this talk, I will focus on the affine diffeomorphism group Aff(S,q) of a half-translation surface (S,q). This is the group of self-diffeomorphisms with constant differential away from the singularities. This group also coincides with the stabiliser of the associated Teichmüller disc under the action of the mapping class group on Teichmüller space. Our main result is that any finitely generated subgroup of Aff(S,q) is undistorted in the mapping class group.

ID：647 1604 0205
Code：112487