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Homological invariants of
codimension $2$ contact submanifolds
Laurent Côté and François-Simon Fauteux-Chapleau |
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Geometry & Topology 28 (2024) 1–125
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DOI: 10.2140/gt.2024.28.1
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Abstract |
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Codimension contact submanifolds are the natural generalization of transverse knots to contact manifolds of arbitrary dimension. We construct new invariants of codimension contact submanifolds. Our main invariant can be viewed as a deformation of the contact homology algebra of the ambient manifold. We describe various applications of these invariants to contact topology. In particular, we exhibit examples of codimension contact embeddings into overtwisted and tight contact manifolds which are formally isotopic but fail to be isotopic through contact embeddings. We also give new obstructions to certain relative symplectic and Lagrangian cobordisms. |
Keywords
codimension 2 contact submanifolds, contact homology
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Mathematical Subject Classification
Primary: 53D10, 53D42
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References |
Publication
Received: 19 December 2020
Revised: 23 January 2022
Accepted: 28 June 2022
Published: 27 February 2024
Proposed: Leonid Polterovich
Seconded: Ciprian Manolescu, Paul Seidel
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Authors |
| Laurent Côté | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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| François-Simon Fauteux-Chapleau | |
| Department of Mathematics Stanford University Stanford, CA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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