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2003 Heegaard Floer homology and alternating knots
Peter Ozsváth, Zoltán Szabó
Geom. Topol. 7(1): 225-254 (2003). DOI: 10.2140/gt.2003.7.225

Abstract

In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y, which is closely related to the Heegaard Floer homology of Y. In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of this description, we determine the knot homology for alternating knots, showing that in this special case, it depends only on the signature and the Alexander polynomial of the knot (generalizing a result of Rasmussen for two-bridge knots). Applications include new restrictions on the Alexander polynomial of alternating knots.

Citation

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Peter Ozsváth. Zoltán Szabó. "Heegaard Floer homology and alternating knots." Geom. Topol. 7 (1) 225 - 254, 2003. https://doi.org/10.2140/gt.2003.7.225

Information

Received: 1 November 2002; Revised: 19 March 2003; Accepted: 20 March 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1083.57013
MathSciNet: MR1988285
Digital Object Identifier: 10.2140/gt.2003.7.225

Subjects:
Primary: 57R58
Secondary: 53D40, 57M25, 57M27

Rights: Copyright © 2003 Mathematical Sciences Publishers

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