Heegaard Floer Homology

We will begin by introducing the necessary ingredients for the definition of Heegaard Floer homology, including Heegaard splittings and diagrams, symmetric products, and holomorphic disks. We will then review the construction of Heegaard Floer homology and its different variations, before discussing some useful computations and applications. If we have time, we will also look at invariants arising from Heegaard Floer homology such as the tau, d or contact invariants.

We will mainly follow ‘An introduction to Heegaard Floer homology’ by Ozsváth and Szabó and the notes form a lecture that Manolescu gave in 2020 for background reading.