Lagrangian concordance is not a symmetric relation

Baptiste Chantraine

Lagrangian concordance is not a symmetric relation

Symplectic Geometry 2013-08-19 v2 Geometric Topology

Authors: Baptiste Chantraine

Abstract

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.

Keywords

legendrian knot theory

Cite

@article{arxiv.1301.3767,
  title  = {Lagrangian concordance is not a symmetric relation},
  author = {Baptiste Chantraine},
  journal= {arXiv preprint arXiv:1301.3767},
  year   = {2013}
}

Comments

18 pages, 12 figures; v2: substantial changes in the exposition, more details in computations of Section 5, accepted for publication in "Quantum Topology"

Lagrangian concordance is not a symmetric relation

Abstract

Keywords

Cite

Comments

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