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Legendrian Contact Homology in P X R

Tobias Ekholm·John Etnyre·Michael G. Sullivan
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Abstract

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

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Tobias Ekholm, John Etnyre, Michael G. Sullivan. 2005-05-21. Legendrian Contact Homology in P X R. https://arxiv.org/abs/math/0505451

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