Legendrian Contact Homology in P X R

Ekholm, Tobias; Etnyre, John; Sullivan, Michael G.

Legendrian Contact Homology in P X R

Authors

Ekholm, Tobias

Etnyre, John

Sullivan, Michael G.

Description

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ 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 $\R^n$ and, more generally, invariants of self transverse immersions into $\R^n$ 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
34 pages, 1 figure