Spectral order for contact manifolds with convex boundary
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 manif...
| Main Authors: | , |
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| Format: | Journal article |
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Mathematical Sciences Publishers
2018
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| _version_ | 1797065051852505088 |
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| author | Juhasz, A Kang, S |
| author_facet | Juhasz, A Kang, S |
| author_sort | Juhasz, A |
| collection | OXFORD |
| description | 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). |
| first_indexed | 2024-03-06T21:23:06Z |
| format | Journal article |
| id | oxford-uuid:4229c0ab-412b-43ea-9449-65186dc9abba |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:23:06Z |
| publishDate | 2018 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:4229c0ab-412b-43ea-9449-65186dc9abba2022-03-26T14:47:50ZSpectral order for contact manifolds with convex boundaryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4229c0ab-412b-43ea-9449-65186dc9abbaSymplectic Elements at OxfordMathematical Sciences Publishers2018Juhasz, AKang, SWe 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). |
| spellingShingle | Juhasz, A Kang, S Spectral order for contact manifolds with convex boundary |
| title | Spectral order for contact manifolds with convex boundary |
| title_full | Spectral order for contact manifolds with convex boundary |
| title_fullStr | Spectral order for contact manifolds with convex boundary |
| title_full_unstemmed | Spectral order for contact manifolds with convex boundary |
| title_short | Spectral order for contact manifolds with convex boundary |
| title_sort | spectral order for contact manifolds with convex boundary |
| work_keys_str_mv | AT juhasza spectralorderforcontactmanifoldswithconvexboundary AT kangs spectralorderforcontactmanifoldswithconvexboundary |