Differential algebra of Legendrian links

By Yu. V. Chekanov. 2002

146 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/555792150410c9eea3ef98a6e10ff5ddfbea870c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Transverse knots and Khovanov homology (2004, background): “transverse knots. Legendrian knots are somewhat better understood and enjoy a rich theory in the context of contact homology and symplectic field theory [ Ch ], [Ng], [EGH]: a differential graded algebra associated to a knot yields new Legendrian knot invariants.”
Legendrian and Transversal Knots (2003, background): “The existence of admissible decompositions has an interesting relation to augmentations of the Chekanov-Eliashberg DGA.”
Framed knot contact homology (2004, background): “Definition 2.3. Let K ⊂ S3 be an oriented knot, and let ∗ be a fixed point on K. A cord of (K, ∗) is any continuous path γ : [0, 1 ] → S3 with γ−1(K) = {0,1} and γ−1({∗}) = ∅. Let AK denote the tensor algebra over Z[λ±1, � ±1] freely generated by the set of homotopy classes of cords of (K, ∗).”
Knot and braid invariants from contact homology II (2003, methodology): “As in [3], we can construct linearized homology groups via this augmentation.”
Topologically Trivial Legendrian Knots (2008, methodology): “The map is not however injective in general (see [ Ch2 , EGH]).”
A Duality Exact Sequence for Legendrian Contact Homology (2008, methodology): “See [ 2 ] for the definition of “stable tame isomorphism”; we will need only some straightforward consequences of the definition, not its precise formulation, in this paper.”
Legendrian fronts for affine varieties (2016, background): “These invariants can be extracted from the Legendrian contact differential graded algebra [20, 28] via the generation criterion [1] and the surgery exact sequences [11, 12].”
Augmentations and rulings of Legendrian knots (2004, background): “In [ 2 ], Chekanov rendered this theory combinatorially computable.”
Floer homology of families I (2003, background): “The homology of this DGA is an invariant of Legendrian isotopy, and has been used in [8] to distinguish Legendrian knots whose classical invariants agree.”
On the equivalence of Legendrian and transverse invariants in knot Floer homology (2011, background): “Among its other achievements, LCH provided the first examples of Legendrian non-simple knot types (Chekanov [7]) and resolved the Legendrian mirror problem (Ng [25]).”
Asymptotic behaviour of holomorphic strips (2001, methodology): “We view the combinatorial definition of the relative contact homology of a Legendrian knot (see Chekanov [ 3 ] and Eliashberg [4]) as a contact anlogue of de Silva’s combinatorial definition of the Floer homology on a Riemann surface.”
Introductory Lectures on Contact Geometry (2001, background): “Shortly after these examples were found an exciting new invariant was discovered [ 5 , 11, 15] that allowed one to find many such “non-simple” Legendrian knots in the standard tight contact structure on S3. The situation for transverse knots is not so well understood: it is unknown whether transvers”
Sectorial descent for wrapped Fukaya categories (2018, background): “In addition, the study of Legendrian contact homology for Legendrian Λ, going back to ideas of Chekanov [13] and Eliashberg [21], can be understood as the study of a partially wrapped Fukaya category with”
Markov theorem for transversal links (2001, unknown): “conjecture has been disproved by Yuriuo Chekanov who has constructed [ 6 ] new invariants of Legendrian knots and has given an example of two Legendrian knots which are topologically isotopic and have equal Thurston-Bennequin and Maslov indices but different Chekanov’s invariants.”