15:30
The handlebody group is defined to be the mapping class group of a handelbody (rel. boundary). It is a subgroup of the mapping class group of the surface of the handlebody, and maps onto the outer automorphism group of its fundamental group (the free group of rank equal to its genus).
Recently Hainaut and Petersen described a subspace of moduli space forming an orbifold classifying space for the handlebody group, and combined this with work of Chan-Galatius-Payne to construct cohomology classes in the group. I will talk about how one can build on their ideas to define a cocompact EG for the handlebody group inside Teichmüller space. This is a manifold with boundary and comes with a filtration by labelled disk systems which we call the `RGB (red-green-blue) disk complex.' I will describe this filtration, use it to describe the boundary of the manifold, and speculate about potential applications to duality results. Based on work-in-progress with Dan Petersen.