Duke Mathematical Journal

Heegaard Floer homology and contact structures

Peter Ozsváth and Zoltán Szabó

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Abstract

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant that takes values in the three-manifold's Floer homology $\widehat{\HF}$. This invariant vanishes for overtwisted contact structures and is nonzero for Stein-fillable ones. The construction uses Giroux's interpretation of contact structures in terms of open-book decompositions.

Article information

Source
Duke Math. J. Volume 129, Number 1 (2005), 39-61.

Dates
First available: 15 July 2005

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1121448863

Digital Object Identifier
doi:10.1215/S0012-7094-04-12912-4

Zentralblatt MATH identifier
1083.57042

Mathematical Reviews number (MathSciNet)
MR2153455

Subjects
Primary: 57R58: Floer homology
Secondary: 53D10: Contact manifolds, general

Citation

Ozsváth, Peter; Szabó, Zoltán. Heegaard Floer homology and contact structures. Duke Mathematical Journal 129 (2005), no. 1, 39--61. doi:10.1215/S0012-7094-04-12912-4. http://projecteuclid.org/euclid.dmj/1121448863.


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