Knot Floer homology and integer surgeries

Abstract

Let $Y$ be a closed three-manifold with trivial first homology, and let $K\subset Y$ be a knot. We give a description of the Heegaard Floer homology of integer surgeries on $Y$ along $K$ in terms of the filtered homotopy type of the knot invariant for $K$. As an illustration of these techniques, we calculate the Heegaard Floer homology groups of non-trivial circle bundles over Riemann surfaces (with coefficients in $\mathbb{Z}∕2\mathbb{Z}$).