Homology cobordism and Heegaard Floer homology

Series
School of Mathematics Colloquium
Time
Thursday, September 19, 2024 - 11:00am for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jen Hom – Georgia Tech – https://jhom6.math.gatech.edu/
Organizer
Alex Dunn, Xiaoyu He, Rose McCarty, Dmitrii Ostrovskii, and Wei Zhu

Under the operation of connected sum, the set of three-manifolds form a monoid. Modulo an equivalence relation called homology cobordism, this monoid (of homology spheres) becomes a group. What is the structure of this group? What families of three-manifolds generate (or don’t generate) this group? We give some answers to these questions using Heegaard Floer homology. This is joint work with (various subsets of) I. Dai, K. Hendricks, M. Stoffregen, L. Truong, and I. Zemke.