Heegaard diagrams and Floer homology

  • Peter S. Ozsváth

    Princeton University, United States
  • Zoltán Szabó

    Princeton University, United States
Heegaard diagrams and Floer homology cover
Download Chapter PDF

A subscription is required to access this book chapter.


We review the construction of Heegaard–Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the case of the Conway link.