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.