Volume 18, issue 6 (2018)

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Spectral order for contact manifolds with convex boundary

András Juhász and Sungkyung Kang

Algebraic & Geometric Topology 18 (2018) 3315–3338

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).

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contact structure, spectral order, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M27, 57R17
Secondary: 57R58
Received: 17 August 2017
Revised: 14 March 2018
Accepted: 25 May 2018
Published: 18 October 2018
András Juhász
Mathematical Institute
University of Oxford
United Kingdom
Sungkyung Kang
Mathematical Institute
University of Oxford
United Kingdom