Lagrangian concordance is not a symmetric relation

2013/01/16 by Chantraine, Baptiste · 2 citations
#53D42 #57M50 #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1301.3767

Abstract

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 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.

Cited by

• Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots
• Double-point enhanced GRID invariants and Lagrangian cobordisms

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