A bordered Legendrian contact algebra

Details A bordered Legendrian contact algebra A bordered Legendrian contact algebra

2012-04-09

arxiv.org/abs/1204.1962v1

Mathematics

Symplectic Geometry

20 pages, 4 figures

Scientific paper

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.

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