#### Volume 8, issue 1 (2008)

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Knot Floer homology and integer surgeries

### Peter S Ozsváth and Zoltán Szabó

Algebraic & Geometric Topology 8 (2008) 101–153
##### 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 $ℤ∕2ℤ$).

##### Keywords
knot Floer homology, surgery theory
Primary: 57M27
Secondary: 57M25
##### Publication
Received: 29 April 2005
Revised: 27 December 2006
Accepted: 7 November 2007
Published: 8 February 2008
##### Authors
 Peter S Ozsváth Department of Mathematics Columbia University New York 1002 USA Zoltán Szabó Department of Mathematics Princeton University New Jersey 08544 USA