## Graduate Geometry, Topology and Dynamics Seminar

Edgar A. Bering IV

UIC

pseudo-Anosov representatives of irreducible mapping classes I

**Abstract:**It is the beginning of the end of GGTDS's reading of Casson and Bleiler. Previously we have seen that a mapping class is either periodic, fixes a collection of curves, or is called irreducible. Looking at the action on the space of laminations, we deduced that an irreducible mapping class fixes a pair of laminations and its action on the boundary of the universal cover has sink-source dynamics related to the fixed laminations. In this talk I will show that every irreducible mapping class has a representative homeomorphism that fixes the stable and unstable laminations set-wise, and introduce the notion of the singular foliation associated to a lamination. This sets the stage for the final talk, next week, where we will present Thurston's result: that every irreducible mapping class has a pseudo-Anosov representative.

Wednesday April 5, 2017 at 3:00 PM in SEO 612