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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).
Keywords: contact structure, spectral order, Heegaard Floer homology
Juhász, András 1 ; Kang, Sungkyung 1
@article{10_2140_agt_2018_18_3315,
author = {Juh\'asz, Andr\'as and Kang, Sungkyung},
title = {Spectral order for contact manifolds with convex boundary},
journal = {Algebraic and Geometric Topology},
pages = {3315--3338},
publisher = {mathdoc},
volume = {18},
number = {6},
year = {2018},
doi = {10.2140/agt.2018.18.3315},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3315/}
}
TY - JOUR AU - Juhász, András AU - Kang, Sungkyung TI - Spectral order for contact manifolds with convex boundary JO - Algebraic and Geometric Topology PY - 2018 SP - 3315 EP - 3338 VL - 18 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3315/ DO - 10.2140/agt.2018.18.3315 ID - 10_2140_agt_2018_18_3315 ER -
%0 Journal Article %A Juhász, András %A Kang, Sungkyung %T Spectral order for contact manifolds with convex boundary %J Algebraic and Geometric Topology %D 2018 %P 3315-3338 %V 18 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3315/ %R 10.2140/agt.2018.18.3315 %F 10_2140_agt_2018_18_3315
Juhász, András; Kang, Sungkyung. Spectral order for contact manifolds with convex boundary. Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3315-3338. doi: 10.2140/agt.2018.18.3315
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