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arxiv: 1301.3767 · v2 · pith:AOI6XRG7new · submitted 2013-01-16 · 🧮 math.SG · math.GT

Lagrangian concordance is not a symmetric relation

classification 🧮 math.SG math.GT
keywords concordancelambdalagrangianlegendrianexistsknotrelationsymmetric
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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. 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.

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