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arXiv · 1301.3767

Lagrangian concordance is not a symmetric relation

Baptiste Chantraine
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Abstract

We provide an explicit example of a non trivial Legendrian knot $Λ$ such that there exists a Lagrangian concordance from $Λ_0$ to $Λ$ where $Λ_0$ is the trivial Legendrian knot. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of $Λ$ to show that no Lagrangian concordance exists in the other direction. This proves that the relation of Lagrangian concordance is not symmetric.

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Baptiste Chantraine. 2013-08-16. Lagrangian concordance is not a symmetric relation. https://arxiv.org/abs/1301.3767

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