Abstract
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.
Citation
Çağrı Karakurt. "Contact structures on plumbed 3-manifolds." Kyoto J. Math. 54 (2) 271 - 294, Summer 2014. https://doi.org/10.1215/21562261-2642395
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