Homological invariants of codimension 2 contact submanifolds

Côté, Laurent¹ ; Fauteux-Chapleau, François-Simon²

¹ Department of Mathematics, Harvard University, Cambridge, MA, United States
² Department of Mathematics, Stanford University, Stanford, CA, United States

Geometry & topology, Tome 28 (2024) no. 1, pp. 1-125.

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.1

Keywords: codimension 2 contact submanifolds, contact homology

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