Lagrangian concordance is not a symmetric relation

Baptiste Chantraine (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We provide an explicit example of a non trivial Legendrian knot Λ such that there exists a Lagrangian concordance from Λ0 to Λ where Λ0 is the trivial Legen-drian knot with maximal Thurston-Bennequin number. 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. Mathematics Subject Classification (2010). 57R17, 53D42, 57M50.

Mots clés: Lagrangian; Legendrian; Cobordism; Contact Homology

Domaines: Géométrie symplectique [math.SG]; Topologie géométrique [math.GT]

Baptiste Chantraine. Lagrangian concordance is not a symmetric relation. Quantum Topology, 2015, 6 (3), pp.451-474. ⟨hal-01135651⟩