Grid diagrams and Heegaard Floer invariants

Abstract

We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in $\mathbb{Z}/2\mathbb{Z}$). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descriptions of the mod $2$ Ozsváth-Szabó mixed invariants of closed four-manifolds, also in terms of grid diagrams.

Authors

Ciprian Manolescu

Department of Mathematics, Stanford University, Stanford, CA, 94305

Peter Ozsváth

Department of Mathematics, Princeton University, Princeton, NJ, 08544

Dylan P. Thurston

Department of Mathematics, Indiana University, Bloomington, IN 47405