Sutured Heegaard diagrams for knots

Abstract

We define sutured Heegaard diagrams for null-homologous knots in 3-manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum. Our result echoes Gabai's earlier works. We also show that for so-called 'semifibred' satellite knots, the top filtration term of the knot Floer homology is isomorphic to the counterpart of the companion.

This is the version published by Algebraic & Geometric Topology on 2 April 2006

References in corpus (3)

• Holomorphic disks and genus bounds
• Longitude Floer homology and the Whitehead double
• On knot Floer homology and cabling

Cited by in corpus (7)

• Knot Floer homology detects fibred knots
• Floer homology and surface decompositions
• Holomorphic discs and sutured manifolds
• Knot Floer homology of Whitehead doubles
• On sutured Floer homology and the equivalence of Seifert surfaces
• Cosmetic surgeries on genus one knots
• Non-separating spheres and twisted Heegaard Floer homology