Legendrian contact homology in $P \times \mathbb{R}$

@article{Ekholm2007LegendrianCH,
  title={Legendrian contact homology in \$P \times \mathbb\{R\}\$},
  author={Tobias Ekholm and Tobias Ekholm and John B. Etnyre and John B. Etnyre and Michael C. Sullivan},
  journal={Transactions of the American Mathematical Society},
  year={2007},
  volume={359},
  pages={3301-3335}
}
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form P x 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 ofR" and, more generally, invariants of self transverse immersions into R n up to restricted regular homotopies. When n = 3, this application is the… 

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