The Legendrian Whitney trick

Abstract

In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.

arXiv comment16 Pages, 5 Figures

References in corpus (7)

• On the classification of tight contact structures I
• Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
• Maximal contact and symplectic structures
• Spaces of Knots
• Convex hypersurface theory in contact topology
• Open book decompositions for contact structures on Brieskorn manifolds
• Embedding all contact 3-manifolds in a fixed contact 5-manifold

Cited by in corpus (4)

• An $h$-principle for embeddings transverse to a contact structure
• Exotic Dehn twists on sums of two contact 3-manifolds
• Homological invariants of codimension 2 contact submanifolds
• On open books and embedding of smooth and contact manifolds