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

John G. Harper (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

Michael G. Sullivan (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

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].

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