Non-loose Legendrian spheres with trivial Contact Homology DGA

Abstract

Loose Legendrian n-submanifolds, for n at least 2, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian isotopic. Legendrian contact homology is a Floer theoretic invariant that associates a differential graded algebra (DGA) to a Legendrian submanifold. The DGA of a loose Legendrian submanifold is trivial.

The main result in the paper is wrong. The Legendrian spheres claimed to be non-loose are in fact loose. The author thanks Emmy Murphy showing that the spheres are loose

References in corpus (4)

• Loose Legendrian embeddings in high dimensional contact manifolds
• Lifting pseudo-holomorphic polygons to the symplectisation of $P\times \mathbb{R}$ and applications
• Knot contact homology
• Legendrian Contact Homology in P X R

Cited by in corpus (7)

• Contact homology and virtual fundamental cycles
• Algebraic Torsion in higher-dimensional contact manifolds
• A note on infinite number of exact Lagrangian fillings for spherical spuns
• Lagrangian fillings and complicated Legendrian unknots
• Nearby Lagrangian fibers and Whitney sphere links
• On existence of non-compact exact lagrangian cobordism
• Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots