Math 235 (Fall 2008)

Topics in Manifold Theory: Heegaard Floer Homology

  • Time and Place: MWF 1-1:50 pm in MS 7608
  • Instructor: Ciprian Manolescu
  • E-mail:
  • Office: MS 6921
  • Office Hours: Fridays 2 - 3:30 pm and by appointment
Heegaard Floer theory, developed by Ozsvath and Szabo, is a powerful technique for studying the key objects in low-dimensional topology: knots and links in the three-sphere, 3- and 4-dimensional manifolds. In particular, it provides answers to the following questions: Given a knot in space, how can we tell if it is the unknot? Given a two-dimensional homology class in a three-manifold, what is the minimal complexity of a surface representing that class? How can one distinguish 4-manifolds that are homeomorphic but not diffeomorphic?

While the questions above can also be answered in different ways, Heegaard Floer theory provides a unified approach to them, as well as to many other problems.

This course is meant as an introduction to low-dimensional topology and Heegaard Floer homology. We will explain both the original definition of the Heegaard Floer invariants (using symplectic geometry), and some of the more recent combinatorial definitions.

Prerequisites: Math 225A (Differentiable Manifolds), Math 225C (Introduction to Algebraic Topology).