Positive isotopies of Legendrian submanifolds and applications

2010/04/29 by Vincent Colin, Colin, Vincent, Emmanuel Ferrand +4 · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.1004.5263

arxiv created 2010/04/29 · openalex publication_date 2010/04/29 · arxiv updated 2010/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold ST^*M, provided that the universal cover of M is \RMⁿ. We consider some related results in the space of one-jets of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manifold.

Cited by

• A survey on orderability and contact non-squeezing

Related

• Positive Legendrian isotopies and Floer Theory
• Legendrian Submanifolds in R²ⁿ⁺¹ and Contact Homology
• Legendrian Contact Homology in P X R
• Loose Legendrian embeddings in high dimensional contact manifolds
• On Legendrian Embbeddings into Open Book Decompositions