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

Ozsváth, Peter; Szabó, Zoltán

doi:10.2140/agt.2008.8.615

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

Peter Ozsváth and Zoltán Szabó

Algebraic & Geometric Topology 8 (2008) 615–692

DOI: 10.2140/agt.2008.8.615

Abstract

The knot Floer homology is an invariant of knots in $S^{3}$ whose Euler characteristic is the Alexander polynomial of the knot. In this paper we generalize this to links in $S^{3}$ giving an invariant whose Euler characteristic is the multi-variable Alexander polynomial. We study basic properties of this invariant, and give some calculations.

Keywords

Floer homology, links, link invariant, multi-variable Alexander polynomial

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 3 February 2003

Revised: 9 November 2007

Accepted: 9 November 2007

Published: 24 May 2008

Authors

Peter Ozsváth
Department of Mathematics Columbia University New York, NY 10027 USA

Zoltán Szabó
Department of Mathematics Princeton University New Jersey 08544 USA

Volume 8, issue 2 (2008)