Lagrangian concordance is not a symmetric relation

  • Baptiste Chantraine

    Université de Nantes, France


We provide an explicit example of a non trivial Legendrian knot such that there exists a Lagrangian concordance from to where 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 to show that no Lagrangian concordance exists in the other direction. This proves that the relation of Lagrangian concordance is not symmetric.

Cite this article

Baptiste Chantraine, Lagrangian concordance is not a symmetric relation. Quantum Topol. 6 (2015), no. 3, pp. 451–474

DOI 10.4171/QT/68