| Abstract |
Puncture-forgetting maps play an important role in the study of Teichmüller spaces, mapping class groups, and curves on surfaces. In my talk at KAIST last winter, I introduced the basic idea of puncture-forgetting maps for measured foliations and outlined the proof of the main result. In this talk, to keep the presentation self-contained, we will begin by reviewing the relevant definitions and the main theorems. We will then discuss recent developments in this theory and present 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. Then, we will also discuss several related questions and directions for future research. This is joint work with Jeremy Kahn. |
