Morse flow trees and Legendrian contact homology in 1-jet spaces

Abstract

Let $L\subset J^1(M)$ be a Legendrian submanifold of the 1-jet space of a Riemannian $n$-manifold $M$. A correspondence is established between rigid flow trees in $M$ determined by $L$ and boundary punctured rigid pseudo-holomorphic disks in $T^{\ast }M$, with boundary on the projection of $L$ and asymptotic to the double points of this projection at punctures, provided $n\le 2$, or provided $n>2$ and the front of $L$ has only cusp edge singularities. This result, in particular, shows how to compute the Legendrian contact homology of $L$ in terms of Morse theory.

118 pages, 21 figures

References in corpus (2)

• Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil
• Knot and braid invariants from contact homology I

Cited by in corpus (15)

• A Duality Exact Sequence for Legendrian Contact Homology
• Duality between Lagrangian and Legendrian invariants
• Legendrian Fronts for Affine Varieties
• Knot contact homology
• A combinatorial DGA for Legendrian knots from generating families
• Generating families and augmentations for Legendrian surfaces
• Knotted Legendrian surfaces with few Reeb chords
• A topological introduction to knot contact homology
• Non-loose Legendrian spheres with trivial Contact Homology DGA
• Filtrations on the knot contact homology of transverse knots
• A note on infinite number of exact Lagrangian fillings for spherical spuns
• Simplicial descent for Chekanov-Eliashberg dg-algebras
• Koszul duality via suspending Lefschetz fibrations
• Calabi-Yau structure on the Chekanov-Eliashberg algebra of a Legendrian sphere
• Geography of bilinearized Legendrian contact homology