  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 Sivek's 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.
