An introduction to Heegaard Floer homology

Instructor: Peter Ozsváth
phone: 609-258-4222
email: petero@math.princeton.edu
office: 1106

Course Assistant: Ollie Thakar

The course:

Heegaard Floer homology is a tool for studying low-dimensional manifolds, using ideas inspired by symplectic geometry. This 3-lecture semi-mini-course will serve as an introduction to these ideas. A loose lecture plan will be to:

Describe the structure of the theory.
Give some motivation for the introduction of the invariants.
Describe variations of the construction, and its relationship with other invariants.

Time permitting, I will also describe constructions in grid homology, where holomorphic aspects of theory can be described in purely combinatorial terms.

Background reading:

J. Milnor Topology from a differentiable point of view, for a rapid and very elegant introduction to differential topology.
Milnor Morse Theory, for further background in topology.
R. Bott and L. P. Tu Differential forms in Algebraic Topology for further reading in topology.

References on low-dimensional topology:

D. Rolfsen Knots and Links.
R. Lickorish An introduction to knot theory.
R. Gompf and A. Stipsicz 4-manifolds and Kirby Calculus.

Background in symplectic geometry:

Morse theory and Floer homology M. Audin and M. Damian.

Surveys on Heegaard Floer homology:

Lecture notes for a series of lectures in similar spirit: An introduction Heegaard Floer homology by Z. Szabó and me.
Further lecture notes Lectures of Heegaard Floer homology by Z. Szabó and me.
More on knot Floer homology An overview of knot Floer homology by Z. Szabó and me.

On the combinatorial theory:

Grid homology for knots and links by A. Stipsicz, Z. Szabó and me, is available here; please go and buy a hard copy, too!