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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Sutured Heegaard diagrams for knots

Yi Ni

Algebraic & Geometric Topology 6 (2006) 513–537

arXiv: math.GT/0507440

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.

Keywords
knot Floer homology, sutured Heegaard diagram, Murasugi sum, semifibred satellite knot
Mathematical Subject Classification 2000
Primary: 57R58, 57M27
Secondary: 53D40
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Publication
Received: 22 July 2005
Revised: 13 January 2006
Accepted: 12 March 2006
Published: 2 April 2006
Authors
Yi Ni
Department of Mathematics
Princeton University
Princeton
NJ 08544
USA