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

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.