Automatic continuity for homeomorphism groups
schedule le mardi 25 avril 2017 de 10h30 à 12h00
Organisé par : D. Burguet, P-A. Guihéneuf
Intervenant : Katie Mann (Katie Mann)
Lieu : Salle Paul Lévy, Campus Jussieu (salle 113, Tour 16/26)
Sujet : Automatic continuity for homeomorphism groups
Many (but not all) examples of real Lie groups G have a unique Lie group structure, meaning that every abstract isomorphism G -> G is necessarily continuous. In this talk, I'll discuss a recent stronger result for groups of homeomorphisms of manifolds: every homomorphism from Homeo(M) to any other separable topological group is necessarily continuous.
This result is part of a broader program. Both the topology and the algebraic structure of groups of homeomorphisms or diffeomorphisms are important objects to understand in dynamics and foliation theory. Automatic continuity is one of a family of results that show the questions of topology and algebraic structure are closely related. I will also discuss some applications to understanding groups acting on manifolds, and to the structure of groups of germs of homeomorphisms, using joint work with F. Le Roux.