An algorithm for computing some Heegaard Floer homologies

Abstract

In this paper, we give an algorithm to compute the hat version of the Heegaard Floer homology of a closed oriented three-manifold. This method also allows us to compute the filtrations coming from a null-homologous link in a three-manifold.

20 pages, 20 figures. The paper used to be known as "A combinatorial description of some Heegaard Floer homologies". Minor changes. This version to appear in Annals of Mathematics

References in corpus (4)

• Floer homology and knot complements
• Floer homology and surface decompositions
• Link Floer homology detects the Thurston norm
• Combinatorial cobordism maps in hat Heegaard Floer theory

Cited by in corpus (10)

• Floer homology and surface decompositions
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Bordered Floer homology for sutured manifolds
• Knot doubling operators and bordered Heegaard Floer homology
• On the spectral sequence from Khovanov homology to Heegaard Floer homology
• A combinatorial description of the $U^2=0$ version of Heegaard Floer homology
• A Simplification of Combinatorial Link Floer Homology
• Holomorphic discs and surgery exact triangles
• Combinatorial proofs for basic properties of Ozsvath-Szabo invariant
• Relative Q-gradings from bordered Floer theory