Monday 2 June 2025
15:00–16:30*

Louis Hainaut (University of Chicago) — A classifying space for the mapping class group of 3-dimensional handlebodies

The mapping class group of 2-dimensional surfaces (of genus g) admits as a classifying space the moduli space ℳ_g. This moduli space also happens to classify various structures of interest that one can consider on a surface (for ex. complex structures, conformal structures, Riemannian metrics,..), and a geometric model for this classifying space is obtained as the quotient of the Teichmuller space by the mapping class group.

In joint work with Dan Petersen, we described a model for the classifying space of the mapping class group of 3-dimensional handlebodies as an explicit open subspace of ℳ_g. After introducing the objects of interest and motivating their study, I will discuss some consequences of our construction and, time permitting, I will present some ideas of the proof that this space is indeed a classifying space.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.