Knot Floer homology and integer surgeries

Ozsváth, Peter; Szabó, Zoltán

doi:10.2140/agt.2008.8.101

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Knot Floer homology and integer surgeries

Peter S Ozsváth and Zoltán Szabó

Algebraic & Geometric Topology 8 (2008) 101–153

DOI: 10.2140/agt.2008.8.101

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 $ℤ ∕ 2 ℤ$ ).

Keywords

knot Floer homology, surgery theory

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M25

References

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

Volume 8, issue 1 (2008)