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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 version of the Legendrian contact algebra of certain Legendrians submanifolds in standard contact $J^1(M).$ This includes all 1- and 2-dimensional Legendrians, and some higher dimensional ones. We present various applications including a Mayer-Vietoris sequence for linearized contact homology similar to Siveks and a connect sum formula for the augmentation variety introduced by Ng. The main tool is the theory of gradient flow trees developed by Ekholm.
We describe a weighted $A_infty$-algebra associated to the torus. We give a combinatorial construction of this algebra, and an abstract characterization. The abstract characterization also gives a relationship between our algebra and the wrapped Fuka
In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to
Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $Lambdasubset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $Lambda$ we get a Weinstein cobordism $X_{Lambda}$ with a collection of Lagra
The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our def
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then