A surgery formula for knot Floer homology

Let K be a rationally null-homologous knot in a 3 -manifold Y, equipped with a non-zero framing, and let Y_ (K) denote the result of -framed surgery on Y. Ozsváth and Szabó gave a formula for the Heegaard Floer homology groups of Y_ (K) in terms of the knot Floer complex of (Y, K). We strengthen this formula by adding a second filtration that computes the knot Floer complex of the dual knot K_ in Y_, i. e. , the core circle of the surgery solid torus. In the course of proving our refinement we derive a combinatorial formula for the Alexander grading which may be of independent interest.