Big Mapping Class Groups in Dimensions 0, 1, and 2

George Domat, Rice University

I'll give a broad introduction to big mapping class groups and why they may be of interest to set theorists. These are a rich class of Polish groups coming from the worlds of low-dimensional topology and geometric group theory. Although they are not defined as such, they all arise as automorphism groups of countable structures. Various tools and properties coming from the fields of descriptive set theory and topological dynamics such as automatic continuity and Rosendal's coarse geometry machinery have proved useful in understanding these groups.

MC 5479