Contents Online

# Journal of Symplectic Geometry

## Volume 12 (2014)

### Number 2

### A bordered Legendrian contact algebra

Pages: 237 – 255

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n2.a2

#### Authors

#### Abstract

In [18], 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 $\mathbb{R}^3$. 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 one- and two-dimensional Legendrians, and some higher-dimensional ones. We present various applications including a Mayer-Vietoris sequence for linearized contact homology similar to [18] and a connect sum formula for the augmentation variety introduced in [16]. The main tool is the theory of gradient flow trees developed in [3].