Algebraic & Geometric Topology

Knot Floer homology and integer surgeries

Peter Ozsváth and Zoltán Szabó

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Abstract

Let Y be a closed three-manifold with trivial first homology, and let KY 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 2).

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 1 (2008), 101-153.

Dates
Received: 29 April 2005
Revised: 27 December 2006
Accepted: 7 November 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796809

Digital Object Identifier
doi:10.2140/agt.2008.8.101

Mathematical Reviews number (MathSciNet)
MR2377279

Zentralblatt MATH identifier
1181.57018

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
knot Floer homology surgery theory

Citation

Ozsváth, Peter; Szabó, Zoltán. Knot Floer homology and integer surgeries. Algebr. Geom. Topol. 8 (2008), no. 1, 101--153. doi:10.2140/agt.2008.8.101. https://projecteuclid.org/euclid.agt/1513796809


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