Braids and combinatorial knot Floer homology

Abstract

We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk open book decomposition for (S^3,ξ_std), we associate a corresponding multi-pointed nice Heegaard diagram. We then describe an explicit algorithm for computing the associated knot Floer homology groups. We compute explicit bounds for the computational complexity of our algorithm and demonstrate that, in many cases, it is significantly faster than the previous approach using grid diagrams.

18 pages, 8 figures

References in corpus (4)

• Floer homology and knot complements
• Corrigendum to "Knot Floer homology detects fibred knots"
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• A Modification of the Sarkar-Wang Algorithm and an Analysis of its Computational Complexity

Cited by in corpus (2)

• Three flavors of twisted invariants of knots
• Transverse braids and combinatorial knot Floer homology