## Figures from this paper

## 11 Citations

Invariants of Legendrian Knots and Decompositions of Front Diagrams

- Mathematics
- 2004

The authors prove that the sufficient condition for the existence of an augmentation of the Chekanov–Eliashberg differential algebra of a Legendrian knot, which is contained in a recent work of the…

Legendrian Grid Number One Knots and Augmentations of Their Differential Algebras

- Mathematics
- 2011

In this article we study the differential graded algebra (DGA) invariant associated to Legendrian knots in tight lens spaces. Given a grid number one diagram for a knot in L(p,q), we show how to…

Product structures for Legendrian contact homology

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2010

Abstract Legendrian contact homology (LCH) is a powerful non-classical invariant of Legendrian knots. Linearization makes the LCH computationally tractable at the expense of discarding nonlinear (and…

A Chekanov–Eliashberg algebra for Legendrian graphs

- MathematicsJournal of Topology
- 2020

We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from Legendrian…

Towards the geography of bilinearized Legendrian contact homology

- Mathematics
- 2019

We study the geography of bilinearized Legendrian contact homology for closed, connected Legendrian submanifolds with vanishing Maslov class in 1-jet spaces. We show that this invariant detects…

Augmentations and ruling polynomials for Legendrian graphs

- Mathematics
- 2019

In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two Legendrian isotopy invariants: augmentation number via point-counting over a finite field,…

Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra

- Mathematics
- 2013

We study satellites of Legendrian knots in R^3 and their relation to the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence…

Legendrian contact homology in the product of a punctured Riemann surface and the real line

- MathematicsJ. Lond. Math. Soc.
- 2016

We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in P×R , where P is a punctured Riemann surface. As an application we show that, for…

Legendrian solid-torus links

- Mathematics
- 2004

Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R 3 , Poincare-Chekanov polynomials and characteristic al-…

Legendrian contact homology in the product of a punctured Riemann surface and the real line

- Mathematics
- 2011

We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in P ×R, where P is a punctured Riemann surface. As an application we show that for…