Legendrian Contact Homology in P × R
نویسندگان
چکیده
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 includes 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.
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