Homological invariants of codimension 2 contact submanifolds

Abstract

Codimension 2 contact submanifolds are the natural generalization of transverse knots to contact manifolds of arbitrary dimension. In this paper, 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.

arXiv comment83 pages; v3: final version

References in corpus (32)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Legendrian knots, transverse knots and combinatorial Floer homology
• Contact homology and virtual fundamental cycles
• Loose Legendrian embeddings in high dimensional contact manifolds
• Intersection theory of punctured pseudoholomorphic curves
• An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves
• Lagrangian concordance of Legendrian knots
• Lectures on Symplectic Field Theory
• Legendrian Fronts for Affine Varieties
• Knot contact homology
• Floer theory for Lagrangian cobordisms
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Lecture notes on stabilization of contact open books
• Augmentations are Sheaves
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families
• On transverse invariants from Khovanov homology
• A Poincaré-Birkhoff theorem for tight Reeb flows on $S^3$
• Open books and the Weinstein conjecture
• On Non-Separating Contact Hypersurfaces in Symplectic 4-Manifolds
• Maximal contact and symplectic structures
• Contact Homology of Orbit Complements and Implied Existence
• Holomorphic curves for Legendrian surgery
• Convex hypersurface theory in contact topology
• The Conley-Zehnder index for a path of symplectic matrices
• Definition of Cylindrical Contact Homology in dimension three
• A topological introduction to knot contact homology
• Holomorphic curves in the presence of holomorphic hypersurface foliations
• Filtrations on the knot contact homology of transverse knots
• The Legendrian Whitney trick
• Contact 3-manifolds, holomorphic curves and intersection theory
• Local and global coincidence homology classes
• Infinite not contact isotopic embeddings in $(S^{2n-1},{\xi }_{\mathrm{std}})$ for $n\ge 4$