A bordered Legendrian contact algebra
Abstract
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 . We prove an analogous result for the holomorphic curve version of the Legendrian contact algebra of certain Legendrians submanifolds in standard contact 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.
Cite
@article{arxiv.1204.1962,
title = {A bordered Legendrian contact algebra},
author = {John G. Harper and Michael G. Sullivan},
journal= {arXiv preprint arXiv:1204.1962},
year = {2012}
}
Comments
20 pages, 4 figures. In this version, Theorem 4.6 on Poincar\'e Polynomials has been removed