Heegaard Floer Homology

 

The aim of this reading group is to provide a concise introduction to Heegaard Floer homology, together with some important computational tools and applications. 
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.

 

Organizers: Rory Morrison and Frieda Kern

Schedule: Tuesdays at 10:30am

Schedule: Tuesday 10:30-12:30, Mathematics and Statistics Building:301

  • (06/10/2026) Heegaard splittings and Heegaard diagrams – Yuhe Zhang
  • (13/10/2026) Heegaard splittings and Morse functions – Yuhe Zhang, Introduction to Lagrangian Floer homology (part 1) – Rory Morrison
  • (20/10/2026) Introduction to Lagrangian Floer homology (part 2) – Rory Morrison
  • (27/10/2026) Spin and spin^c structures – Leonardo Migliorini
  • (03/11/2026) Symmetric products and the tautological correspondence
  • (10/11/2026) The Heegaard Floer chain complexes – Chiara Donatone
  • (11/11/2026) The Atiyah-Floer conjecture – Dan Phillips