Algebraic & Geometric Topology

Spectral order for contact manifolds with convex boundary

András Juhász and Sungkyung Kang

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We extend the Heegaard Floer homological definition of spectral order for closed contact 3–manifolds due to Kutluhan, Matić, Van Horn-Morris, and Wand to contact 3–manifolds with convex boundary. We show that the order of a codimension-zero contact submanifold bounds the order of the ambient manifold from above. As the neighborhood of an overtwisted disk has order zero, we obtain that overtwisted contact structures have order zero. We also prove that the order of a small perturbation of a Giroux 2π–torsion domain has order at most two, hence any contact structure with positive Giroux torsion has order at most two (and, in particular, a vanishing contact invariant).

Article information

Algebr. Geom. Topol., Volume 18, Number 6 (2018), 3315-3338.

Received: 17 August 2017
Revised: 14 March 2018
Accepted: 25 May 2018
First available in Project Euclid: 27 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 57R17: Symplectic and contact topology
Secondary: 57R58: Floer homology

contact structure spectral order Heegaard Floer homology


Juhász, András; Kang, Sungkyung. Spectral order for contact manifolds with convex boundary. Algebr. Geom. Topol. 18 (2018), no. 6, 3315--3338. doi:10.2140/agt.2018.18.3315.

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