Rachael Boyd

Classifying spaces for 3-manifold diffeomorphisms

I will talk about joint work with Corey Bregman and Jan Steinebrunner, in which we study the moduli space B Diff(M), for M a compact, connected, reducible 3-manifold, possibly with boundary. Milnor showed that M admits a decomposition as a connected sum of prime manifolds, unique up to reordering the factors. We parametrize these decompositions on the level of embedded spheres in M, which allows us to build computable models for the classifying spaces B Diff(M) and B Diff(M rel ∂M). When ∂M is nonempty, we use this to show B Diff(M rel ∂M) has finite homotopy type, confirming a conjecture of Kontsevich. We also compute the rational cohomology of B Diff ((S^1 x S^2) # (S^1 x S^2)).