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

By T. Ekholm, John B. Etnyre, Michael C. Sullivan. 2007

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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 first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/90a4af3ce49c5665328d7706cb8f0f82dca4cb1f

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Citations in the corpus

Immersed Lagrangian Floer Theory (2008, methodology): “In particular, for (M, ω) exact one can compare our HF∗(L, b;�Znov) for embedded Legendrians in M × S1, and Ekholm et al.’s HC∗(L, J) for embedded Legendrians L in M × R, [ 7 ].”