Towards placing some of the material from Artem Kotelskiy’s talk in context, I will discuss some older joint work with Jonathan Hanselman and Jake Rasmussen. This will centre on the following result: A closed orientable three-manifold containing a separating torus has (the hat version of it's) Heegaard Floer homology of dimension at least 5. The talk aims to give and overview of the proof and discuss consequences, and perhaps even tie in with Jake Rasmussen’s talk, which opened the conference.
This talk was part of the conference "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021