Algebraic & Geometric Topology

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

Peter Ozsváth and Zoltán Szabó

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796839

Digital Object Identifier
doi:10.2140/agt.2008.8.615

Mathematical Reviews number (MathSciNet)
MR2443092

Zentralblatt MATH identifier
1144.57011

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

Keywords
Floer homology links link invariant multi-variable Alexander polynomial

Citation

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. https://projecteuclid.org/euclid.agt/1513796839


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