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Math 236: Heegaard Floer homology

Winter 2021

Instructor: Sucharit Sarkar.
Class: MWF 11:00-11:50, Zoom (link posted on CCLE).
Office hrs: MF 10:00-11:00 (same Zoom link).

Exams and grading: There will be a final take-home exam (total time 24hr) for all the students who require a grade at the end of the course, and the grade will be recorded in CCLE.

Topics: Heegaard Floer homology. This is a fairly recent and extremely active field of research in low-dimensional topology. It associates new homology theories to 3-manifolds and knots and links inside them, and these invariants carry a lot of geometric information about the underlying objects; the theory has been extended for 2-manifolds and 4-manifolds as well. Being recent, there are no good books on the topic. So we will cover (a subset of) the material from the following sources (arranged chronologically).

Lecture notes:

• An introduction to Heegaard Floer homology (Ozsvath-Szabo)
• Lectures on Heegaard Floer homology (Ozsvath-Szabo)
• An introduction to knot Floer homology (Manolescu)
• Heegaard Floer homologies: lecture notes (Lipshitz)
• Lecture notes on Heegaard Floer homology (Hom)

Original Ozsvath-Szabo papers:

• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and three-manifold invariants: properties and applications
• Holomorphic triangles and invariants for smooth four-manifolds
• Holomorphic disks and knot invariants