Legendrian Contact Homology in P X R

By T. Ekholm, John B. Etnyre, Michael C. Sullivan. 2005

115 citations recorded by the source corpus.

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

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

View Paper: https://www.semanticscholar.org/paper/230b36a21fcd8cc9fdb400c34f6a05251d38479e

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Citations in the corpus

Knot contact homology (2011, background): “This result is stated and proven in [17] for the homology-commutative quotient, but the proof there extends verbatim to the full non-commutative algebra.”
Immersed Lagrangian Floer Theory (2008, methodology): “’s HC∗(L, J) for embedded Legendrians L in M×R, [7].”
Rational symplectic field theory over Z2 for exact Lagrangian cobordisms (2006, background): “where 2n = dim(X), μ denotes the Maslov index, and m is the number of punctures (see [10, 13]).”
Legendrian ambient surgery and Legendrian contact homology (2012, methodology): “Both the construction and the invariance have been worked out in the case (J1(R1), λ0) by Chekanov [Che], and in arbitrary contactisations (P × R, dz+ θ) by Ekholm, Etnyre and Sullivan [EES3], where (P, dθ) is an exact symplectic manifold having finite geometry at infinity.”