CMSA Math-Science Literature Lecture: A personal story of the 4D Poincare conjecture

09/28/2020 12:30 pm - 2:00 pm

Michael Freedman (Microsoft – Station Q)

Title: A personal story of the 4D Poincare conjecture

Abstract:  The proof of PC4 involved the convergence of several historical streams.  To get started: high dimensional manifold topology (Smale), a new idea on how to study 4-manifolds (Casson), wild “Texas” topology (Bing). Once inside the proof: there are three submodules: Casson towers come to life (in the sense of reproduction), a very intricate explicit shrinking argument (provided by Edwards), and the “blind fold” shrinking argument (which in retrospect is in the linage of Brown’s proof of the Schoenflies theorem). Beyond those mentioned: Kirby, Cannon, Ancel, Quinn, and Starbird helped me understand my proof. I will discuss the main points and how they fit together.

Talk Chair: Peter Kronheimer