An introduction to Heegaard Floer homology
Instructor: Peter Ozsváth
Course Assistant: Ollie Thakar
Heegaard Floer homology is a tool for studying low-dimensional
manifolds, using ideas inspired by symplectic geometry. This
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.
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:
On the combinatorial theory: