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Spectral order for
contact manifolds with convex boundary
András Juhász and Sungkyung Kang |
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Algebraic & Geometric Topology 18 (2018) 3315–3338
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Abstract |
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We extend the Heegaard Floer homological definition of spectral order for closed contact –manifolds due to Kutluhan, Matić, Van Horn-Morris, and Wand to contact –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 –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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Keywords
contact structure, spectral order, Heegaard Floer homology
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Mathematical Subject Classification 2010
Primary: 57M27, 57R17
Secondary: 57R58
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References |
Publication
Received: 17 August 2017
Revised: 14 March 2018
Accepted: 25 May 2018
Published: 18 October 2018
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Authors |
| András Juhász | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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| Sungkyung Kang | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
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