Geometry & Topology Seminar: "Punctured mapping class group actions on the circle"

Abstract: The mapping class group of a surface S with a marked point can be identified with the group Aut(pi_1(S)) of automorphisms of the fundamental group of the surface. I will explain a new rigidity theorem, joint with M. Wolff, that shows that any nontrivial action of Aut(pi_1(S)) on the circle is semi-conjugate to its natural action on the Gromov boundary of pi_1(S); solving a problem posed by Farb. As a consequence, we can also quickly recover and extend some older results on the regularity (non-smoothability) of these group actions.

Host: Steven Frankel