An algorithm for computing some Heegaard Floer homologies

2010/03/25 by Sucharit Sarkar, Jiajun Wang · 123 citations
Mathematics · Medicine · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Botulinum Toxin and Related Neurological Disorders #Floer homology #Mathematics #Heegaard splitting #Manifold (fluid mechanics) #3-manifold #Algorithm #Homology (biology) #Null (SQL) #Topology (electrical circuits) #Combinatorics #Pure mathematics #Computer science

paper · pdf · doi:10.4007/annals.2010.171.1213

published in Annals of Mathematics 171(2), 1213-1236 (Princeton University)

openalex publication_date 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

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

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Holomorphic disks and three-manifolds invariants: Properties and applications
• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and genus bounds
• A combinatorial description of knot Floer homology
• Knot Floer homology detects fibred knots

Cited by

• Topological algebra of symplectic geometry of symmetric powers
• Floer homology and surface decompositions
• A surgery triangle for lattice cohomology
• A flexible construction of equivariant Floer homology and applications
• Building Foliations from Heegaard Diagrams
• Floer homology [wikipedia]

Related

• An algorithm for computing some Heegaard Floer homologies
• An algorithm to compute some Heegaard Floer homologies
• Combinatorial Heegaard Floer homology and nice Heegaard diagrams
• Introduction to the basics of Heegaard Floer homology
• Heegaard diagrams and Floer homology