Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots

By J. Epstein, Dmitry Fuchs, Maike Meyer. 2001

78 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3161b9239146debad09f187f73bbfe5968b4c227

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

1. Zolt'an Szab'o
2. Peter S. Ozsv'ath
3. A. Stipsicz
4. P. Lisca
5. Dylan Thurston
6. Lenhard L. Ng
7. John B. Etnyre
8. Ian Zemke

In Geometry and Topology

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. Zolt'an Szab'o
4. P. Lisca
5. Lenhard L. Ng
6. John B. Etnyre
7. Dylan Thurston
8. John A. Baldwin

In Mathematical Physics

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. P. Lisca
4. Zolt'an Szab'o
5. Lenhard L. Ng
6. John B. Etnyre
7. Dylan Thurston
8. John A. Baldwin

Citations in the corpus

• Computable Legendrian invariants (2000, background): “of a Legendrian knot K over Z/2, graded over Z/(2r(K)); let C = A/I be its characteristic algebra. We first review the definition of the Poincar´e-Chekanov polynomials. The following term is taken from [EFM]. Definition 3.5. Let (A,∂) be a DGA over Z/2. An algebra map ε : A → Z/2 is an augmentation if ”
• Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, background): “By [9, 13], up to negative stabilizations the Legendrian knot L only depends on the transverse isotopy class of T .”
• Transverse knots distinguished by knot Floer homology (2007, background): “Indeed, the set of transverse knots up to transverse isotopy is naturally identified, through the correspondence L ↔ L, with the set of Legendrian knots up to Legendrian isotopy and negative stabilization [11].”
• Legendrian and Transversal Knots (2003, background): “23 (In (R(3), ξstd), Epstein, Fuchs and Meyer 2001, [31]; In a general contact manifold, Etnyre and Honda 2001, [38]).”
• Markov theorem for transversal links (2001, unknown): “Some examples of even finer type have been found in [ 9 ].”
• Contact surgeries and the transverse invariant in knot Floer homology (2008, background): “The result was extended in [ 5 ] for all Eliashberg–Chekanov knots En (n ≥ 3). Notice that the DGA used in these proofs vanish for stabilized knots, hence generally it cannot be used to distinguish Legendrian approximations of transverse knots.”
• Grid Homology for Knots and Links (2015, background): “(Note that our convention differs from the one of [43]: we work with the contact structure given by the one-form α = dz−ydx, while in the reference the contact structure is given by ydx−dz = −α, giving different orientations in certain statements.”
• Knot and braid invariants from contact homology II (2003, methodology): “research. Holomorphic curve techniques stemming from the introduction of Symplectic Field Theory [7] have inspired a great deal of work on Legendrian isotopy invariants; papers in the subject include [3, 5, 6, 8, 9, 18, 23], among others. Most of these papers focus on Legendrian knots, and all deduc”