Forgetting Punctures in Measured Foliations and Dynamics on the Universal Curve over Teichmuller Space
ABSTRACT
Puncture-forgetting maps play an important role in the study of Teichmüller spaces, mapping class groups, and curves on surfaces. In this talk, I will discuss several ways of forgetting punctures for measured foliations.
The original motivation comes from the dynamics of post-critically finite rational maps on the Riemann sphere, which I discussed in a talk at KIAS two years ago. I will describe recent developments in this theory and a new application to the universal curve over Teichmüller space, viewed as the (infinite-volume) quotient of Teichmüller space by the point-pushing mapping class group. I will also discuss several related questions and directions for future research.
This is joint work with Jeremy Kahn.
