Seminar organizers: William Chong, Katherine Goldman, Christopher Karpinski, Carl Kristof-Tessier, Piotr Przytycki, Daniel Wise
I will talk about joint work with Corey Bregman and Jan Steinebrunner, in which we study the moduli space $\text{BDiff}(M)$, for M a compact, connected, reducible 3-manifold. We prove that when $M$ is orientable and has non-empty boundary, $\text{BDiff}(M\text{ rel } ∂M)$ has the homotopy type of a finite CW-complex. This was conjectured by Kontsevich and previously proved in the case where $M$ is irreducible by Hatcher and McCullough. The theory we develop to prove this theorem has other applications, and I'll provide an overview of these.