Corey Bregman, Tufts University
Event Date
2026-02-04
Event Time
03:30 pm ~ 04:30 pm
Event Location
Wachman Hall, room 407
Abstract: Let $M$ be an orientable 3-manifold. A celebrated theorem of Kneser-Milnor states that $M$ admits a unique connected sum decomposition, up to permutations of the prime factors. We prove a space-level version of this theorem by introducing a poset of decompositions of $M$ along collections of essential 2-spheres (called separating systems) and showing that the geometric realization of this poset is contractible. As an application, we prove that for any $M$ the classifying space $BDiff(M)$ is homotopy equivalent to a CW complex with finite $k$-skeleton for every $k$. When M is a connected sum of $g$ copies of $S^1 \times S^2$, we also show that every topological $M$-bundle fiberwise extends to a bundle of 4-dimensional handlebodies, generalizing another classical result due to Laudenbach-Poenaru. This is joint work with Rachael Boyd and Jan Steinebrunner.