Legendrian Contact Homology in P X R

2005/05/21 by Tobias Ekholm, Ekholm, Tobias, John Etnyre +3 · 2 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.math/0505451

34 pages, 1 figure

arxiv created 2005/05/21 · arxiv updated 2009/12/01

Abstract

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P× \R where P is an exact symplectic manifold is established. The class of such contact manifolds include 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of \Rⁿ and, more generally, invariants of self transverse immersions into \Rⁿ up to restricted regular homotopies. When n=3, this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng

Cited by

• Submanifolds in contact geometry
• Augmentation categories in higher dimensions

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