Speaker: Matthew Stoffregen, Massachusetts Institute of Technology

Title: Smooth 4-manifolds and the geometry of 3-manifolds

Date: 12/10/2019

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

One of the interests of low-dimensional topologists is understanding which smooth 4-manifolds can bound a given 3-manifold, or, as a special case, understanding the set of 3-manifolds up to so-called homology cobordism (to be defined in the talk). This question turns out to have applications to the study of triangulations of high-dimensional manifolds, and is a natural proving ground for Floer-theoretic techniques of studying 3-manifolds. In this talk, we will give some structure theorems about the homology cobordism group, and show that there are three-manifolds that are very far from having any of the seven non-hyperbolic Thurston geometries. This talk includes joint work with I. Dai, K. Hendricks, J. Hom, L. Truong, and I. Zemke.