Related papers: An L-infinity structure for Legendrian contact hom…

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…

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…

Let L be a Legendrian knot in R^3 with the standard contact structure. In [10], a map was constructed from equivalence classes of Morse complex sequences for L, which are combinatorial objects motivated by generating families, to homotopy…

We review and develop the general properties of $L_\infty$ algebras focusing on the gauge structure of the associated field theories. Motivated by the $L_\infty$ homotopy Lie algebra of closed string field theory and the work of Roytenberg…

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary…

Legendrian contact homology (LCH) and its associated differential graded algebra are powerful non-classical invariants of Legendrian knots. Linearization makes the LCH computationally tractable at the expense of discarding nonlinear (and…

To any manifold equipped with a higher degree closed form, one can associate an L-infinity algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we…

For any L-infinity algebra L, we construct an A-infinity structure on the space of symmetric tensors Sym*(L), which generalizes the classical universal enveloping for Lie algebras. Our construction is based on an invariant homotopy on a…

The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory.…

Using the theory of extensions of L-infinity algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the Chevalley-Eilenberg and Harrison…

We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knots in the standard contact R^3 and a relative version of Eliashberg and Hofer's Contact Homology. We use this translation to transport the idea…

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…

Let $L$ be a line bundle over $M$. In this paper we associate an $L_\infty$-algebra to any $L$-Courant algebroid (contact Courant algebroid in the sense of Grabowski). This construction is similar to the work of Roytenberg and Weinstein for…

The Chekanov-Eliashberg differential graded algebra of a Legendrian knot L is a rich source of Legendrian knot invariants, as is the theory of generating families. The set P(L) of homology groups of augmentations of the Chekanov-Eliashberg…

Given a Legendrian knot $\Lambda \subset \mathbb{R}^3$ and a vertical line dividing the front projection of $\Lambda$ into two halves, we construct a differential graded algebra associated to each half-knot. We then show that one may obtain…

I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I…

We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that $(TM, T^*M)$ has a canonical structure of…

This is the second in a sequence 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 first define the…

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…

In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded…