Related papers: Augmentation varieties and disk potentials II
In this paper, we consider exact Lagrangian cobordisms and the map they induce on the Chekanov-Eliashberg DGAs of their Legendrian ends as defined by Ekholm, Honda, and Kalman. Specifically, we show how to adapt this map to linearizations…
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 contact homology. The construction is…
This is the third in a series of papers in which we construct Chekanov-Eliashberg algebras for Legendrians in circle-fibered contact manifolds and study the associated augmentation varieties. In this part, we prove that for connected…
For an exact symplectic manifold $M$ and a Legendrian submanifold $\Lambda$ of the contactification $M\times \mathbb{R}$, we construct the augmentation category (over a field of characteristic 2), a unital $A_\infty$-category whose objects…
In this note we construct augmentations of Chekanov-Eliashberg algebras of certain high dimensional Legendrian submanifolds that are not induced by exact Lagrangian fillings. The obstructions to the existence of exact Lagrangian fillings…
This is the first in a sequence of papers where we show that Lagrangian fillings such as the Harvey-Lawson filling in any dimension define augmentations of Chekanov-Eliashberg differential graded algebras by counting configurations of…
In this paper we construct an $\mathcal{A}_\infty$-category associated to a Legendrian submanifold of jet spaces. Objects of the category are augmentations of the Chekanov algebra $\mathcal{A}(\Lambda)$ and the homology of the morphism…
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, for the augmentation variety of the…
In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_{\infty}$-category, which lifts the set of…
This is an introduction to Legendrian contact homology and the Chekanov-Eliashberg differential graded algebra, with a focus on the setting of Legendrian knots in $\mathbb{R}^3$. This is the published version of the paper, but with a…
The Chekanov-Eliashberg dg-algebra is an algebraic invariant of Legendrian submanifolds of contact manifolds, whose definition recently has been extended to singular Legendrians. We describe a way of constructing simpler models of this…
Any link that is the closure of a positive braid has a natural Legendrian representative. These were introduced in an earlier paper, where their Chekanov--Eliashberg contact homology was also evaluated. In this paper we re-phrase and…
Given a front projection of a Legendrian knot $K$ in $\mathbb{R}^{3}$ which has been cut into several pieces along vertical lines, we assign a differential graded algebra to each piece and prove a van Kampen theorem describing the…
Sivek proves a "van Kampen" decomposition theorem for the combinatorial Legendrian contact algebra (also known as the Chekanov-Eliashberg algebra) of knots in standard contact $\R^3$ . We prove an analogous result for the holomorphic curve…
We apply the barcodes of persistent homology theory to the Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. We do not require the full Chekanov-Eliashberg algebra to…
We show that if a Legendrian knot in standard contact ${\bb R}^3$ possesses a generating family then there exists an augmentation of the Chekanov-Eliashberg DGA so that the associated linearized contact homology (LCH) is isomorphic to…
We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in…
Consider a pair $(X,L)$, of a Weinstein manifold $X$ with an exact Lagrangian submanifold $L$, with ideal contact boundary $(Y,\Lambda)$, where $Y$ is a contact manifold and $\Lambda\subset Y$ is a Legendrian submanifold. We introduce the…
In this short note, we provide a criterion for DGA-homotopy of augmentations of Chekanov-Eliashberg algebra of disconnected Legendrian submanifolds. We apply the criterion to obtain the extension of geography results of Bourgeois and Galant…
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the…