Invariants of Legendrian Knots and Decompositions of Front Diagrams

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Obstructions to Lagrangian concordance (2014, unknown): “If Λ ≺ U then Theorem 2.4 says that S(Λ,∆2) ≺ S(U,∆2), and then Proposition 2.1 provides a morphism AS(U,∆2) → AS(Λ,∆2) between the Legendrian contact homology DGAs of the two satellites over F = Z/2Z.”
Augmentations and rulings of Legendrian knots (2004, result): “The central result of this paper is the converse, which Fuchs and Ishkhanov have proved independently, using different methods, in [12]: Theorem 1.2.”
Contact homology and one parameter families of Legendrian knots (2004, background): “Do the same in the backward direction, resulting 13Fuchs and Ishkhanov [19] and independently Sabloff [25] have also proven that the existence of an augmentation implies the existence of a ruling.”
A Duality Exact Sequence for Legendrian Contact Homology (2008, background): “In dimension three, however, the theory of the existence of augmentations has been well-studied (see [13, 14, 21, 24, 25]), while less work has been done in higher dimensions.”
Legendrian and Transversal Knots (2003, unknown): “Very recently Fuchs and Ishkhanov, and independently Sabloff, have found a converse to the above theorem.”