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Quantum Topology

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Volume 6, Issue 3, 2015, pp. 451–474
DOI: 10.4171/QT/68

Published online: 2015-08-26

Lagrangian concordance is not a symmetric relation

Baptiste Chantraine[1]

(1) Université de Nantes, France

We provide an explicit example of a non trivial Legendrian knot $\Lambda$ such that there exists a Lagrangian concordance from $\Lambda_0$ to $\Lambda$ where $\Lambda_0$ is the trivial Legendrian knot with maximal Thurston–Bennequin number. We then use the map induced in Legendrian contact homology by a concordance and the augmentation category of $\Lambda$ to show that no Lagrangian concordance exists in the other direction. This proves that the relation of Lagrangian concordance is not symmetric.

Keywords: Lagrangian, Legendrian, cobordism, contact homology

Chantraine Baptiste: Lagrangian concordance is not a symmetric relation. Quantum Topol. 6 (2015), 451-474. doi: 10.4171/QT/68