Algebraic & Geometric Topology

Spectral order for contact manifolds with convex boundary

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 $2π$–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

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

Dates
Revised: 14 March 2018
Accepted: 25 May 2018
First available in Project Euclid: 27 October 2018

https://projecteuclid.org/euclid.agt/1540605644

Digital Object Identifier
doi:10.2140/agt.2018.18.3315

Mathematical Reviews number (MathSciNet)
MR3868222

Zentralblatt MATH identifier
06990065

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

Citation

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. https://projecteuclid.org/euclid.agt/1540605644

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