COMBINATORIAL FLOER HOLMOLOGY

Ciprian Manolescu
Columbia University

Heegaard Floer theory is an important tool in low-dimensional topology, and can be used to address questions about knots, three-manifolds, and four-manifolds. It was developed by Ozsvath and Szabo as a replacement for gauge theory. The original definition involved counting solutions to some nonlinear PDE's. I will present an alternate, purely combinatorial description of Heegaard Floer homology for knots and links in the three-sphere (joint work with Ozsvath and Sarkar), as well as some other related results.