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