Étienne Ghys (ENS Lyon)

Title:

Homeomorphisms of the sphere

Abstract:

Groups of diffeomorphisms of compact manifolds have been a central object of study for many years. In this talk, I aim to provide an overview of some classical results, tracing their origins back to the 1970s. I will also highlight a recent result by D. Cristofaro-Gardiner, V. Humiliere, and S. Seyfaddini. One particularly surprising result is that the group of homeomorphisms of the 2-sphere, preserving both area and orientation, is not a simple group. This is truly remarkable, making the proof a tour de force! My presentation will be impressionistic, hopefully accessible to a wide audience. Rather than delving into technical details, my goal will be more to convince the audience that the problem and its solution are fascinating.