|Location:||MSRI: Simons Auditorium|
To what extent does the algebraic structure of a topological group determine its topology? 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 show a strictly stronger result for groups of homeomorphisms of manifolds: every abstract homomorphism from Homeo(M) to any other separable topological group is necessarily continuous.
Along the way, I'll introduce some beautiful and classical properties of groups of homeomorphisms. This talk should be accessible to everyone.