Effective computation of knot Floer homology

2008/03/17 by Jean-Marie Droz, Droz, Jean-Marie
Mathematics · Medicine · #57M27 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0803.2379

openalex publication_date 2008/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend an approach of Beliakova for computing knot Floer homology and implement it in a publicly available computer program. We review the main programming and optimization methods used. Our program is then used to check that the Floer homology of a prime non-alternating knot with less than 12 crossings has no torsion.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds

Related

• Computations of Heegaard-Floer knot homology
• Knot Floer homology of (1,1)-knots
• An overview of knot Floer homology
• Braids and combinatorial knot Floer homology
• An introduction to knot Floer homology