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Homological invariants of codimension $2$ contact submanifolds

Laurent Côté and François-Simon Fauteux-Chapleau

Geometry & Topology 28 (2024) 1–125
Abstract

Codimension 2 contact submanifolds are the natural generalization of transverse knots to contact manifolds of arbitrary dimension. We construct new invariants of codimension 2 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 2 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
Mathematical Subject Classification
Primary: 53D10, 53D42
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
Authors
Laurent Côté
Department of Mathematics
Harvard University
Cambridge, MA
United States
François-Simon Fauteux-Chapleau
Department of Mathematics
Stanford University
Stanford, CA
United States

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