Algebraic & Geometric Topology

Holomorphic disks, link invariants and the multi-variable Alexander polynomial

Peter Ozsváth and Zoltán Szabó

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The knot Floer homology is an invariant of knots in S3 whose Euler characteristic is the Alexander polynomial of the knot. In this paper we generalize this to links in S3 giving an invariant whose Euler characteristic is the multi-variable Alexander polynomial. We study basic properties of this invariant, and give some calculations.

Article information

Algebr. Geom. Topol., Volume 8, Number 2 (2008), 615-692.

Received: 3 February 2003
Revised: 9 November 2007
Accepted: 9 November 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Floer homology links link invariant multi-variable Alexander polynomial


Ozsváth, Peter; Szabó, Zoltán. Holomorphic disks, link invariants and the multi-variable Alexander polynomial. Algebr. Geom. Topol. 8 (2008), no. 2, 615--692. doi:10.2140/agt.2008.8.615.

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