Kyoto Journal of Mathematics

Contact structures on plumbed 3-manifolds

Çağrı Karakurt

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Abstract

We show that the Ozsváth–Szabó contact invariant c+(ξ)HF+(Y) of a contact 3-manifold (Y,ξ) can be calculated combinatorially if Y is the boundary of a certain type of plumbing X and if ξ is induced by a Stein structure on X. Our technique uses an algorithm of Ozsváth and Szabó to determine the Heegaard–Floer homology of such 3-manifolds. We discuss two important applications of this technique in contact topology. First, we show that it simplifies the calculation of the Ozsváth–Stipsicz–Szabó obstruction to admitting a planar open book for a certain class of contact structures. We also define a numerical invariant of contact manifolds that respects a partial ordering induced by Stein cobordisms. Using this technique, we do a sample calculation showing that the invariant can get infinitely many distinct values.

Article information

Source
Kyoto J. Math., Volume 54, Number 2 (2014), 271-294.

Dates
First available in Project Euclid: 2 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1401741279

Digital Object Identifier
doi:10.1215/21562261-2642395

Mathematical Reviews number (MathSciNet)
MR3215568

Zentralblatt MATH identifier
1300.57026

Subjects
Primary: 57R17: Symplectic and contact topology
Secondary: 57R58: Floer homology 57R65: Surgery and handlebodies 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

Citation

Karakurt, Çağrı. Contact structures on plumbed 3-manifolds. Kyoto J. Math. 54 (2014), no. 2, 271--294. doi:10.1215/21562261-2642395. https://projecteuclid.org/euclid.kjm/1401741279


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