Spectral order for contact manifolds with convex boundary

Juhász, András; Kang, Sungkyung

doi:10.2140/agt.2018.18.3315

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Spectral order for contact manifolds with convex boundary

András Juhász and Sungkyung Kang

Algebraic & Geometric Topology 18 (2018) 3315–3338

DOI: 10.2140/agt.2018.18.3315

Abstract

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 $2 π$ –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).

Keywords

contact structure, spectral order, Heegaard Floer homology

Mathematical Subject Classification 2010

Primary: 57M27, 57R17

Secondary: 57R58

References

Publication

Received: 17 August 2017

Revised: 14 March 2018

Accepted: 25 May 2018

Published: 18 October 2018

Authors

András Juhász
Mathematical Institute University of Oxford Oxford United Kingdom

Sungkyung Kang
Mathematical Institute University of Oxford Oxford United Kingdom

Volume 18, issue 6 (2018)