Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 54, Number 2 (2014), 271-294.
Contact structures on plumbed 3-manifolds
We show that the Ozsváth–Szabó contact invariant of a contact -manifold can be calculated combinatorially if is the boundary of a certain type of plumbing and if is induced by a Stein structure on . Our technique uses an algorithm of Ozsváth and Szabó to determine the Heegaard–Floer homology of such -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.
Kyoto J. Math., Volume 54, Number 2 (2014), 271-294.
First available in Project Euclid: 2 June 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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