Chekanov–Eliashberg invariant of Legendrian knots: existence of augmentations

By Dmitry Fuchs. 2003

98 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/114ad870143e5f45dacefef3c50c2c942467620b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

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.”
Obstructions to Lagrangian concordance (2014, background): “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.”
Lagrangian cobordisms via generating families: Construction and geography (2014, unknown): “While the description of these examples follows the “bottom up” construction specified by the handle attachment of the previous section, we note that these examples were discovered by working “top down” from the resulting links, using graded normal rulings to keep track of which pairs of critical po”
Legendrian knots and exact Lagrangian cobordisms (2012, methodology): “. Dipped diagrams. In this subsection we explain how to modify a Legendrian link Λ with a contractible Reeb chord a so that a becomes simple. The modiﬁcation is called dipping, which ﬁrst appeared in [F] under the name “splashing” and was used extensively in [Sa2]. Lemma 6.22. Let Λ be a Legendrian ”
A Legendrian Thurston-Bennequin bound from Khovanov homology (2005, background): “We remark that an admissible 0-resolution of a front constitutes an ungraded normal ruling (or proper decomposition) of the front in the sense of [4, 9].”
Augmentations and rulings of Legendrian knots (2004, background): “The goal of this paper is to strengthen a connection, discovered by Fuchs [11], between the ability to linearize the contact homology DGA and the non-vanishing of Chekanov’s count of rulings for Legendrian knots in the standard contact R3.”
Generating families and Legendrian contact homology in the standard contact space (2008, methodology): “In the discussion surrounding the definition of e we have proved Lemma 5.4 e is an augmentation of A( F ).”
Contact homology and one parameter families of Legendrian knots (2004, methodology): “In the case of a braid closure, it would be impractical to pull back Fuchs’ augmentation to the original diagram.”