Doubly slice knots and obstruction to Lagrangian concordance
Symplectic Geometry
2023-02-24 v2 Geometric Topology
Abstract
In this short note we observe that a result of Eliashberg and Polterovitch allows to use the doubly slice genus as an obstruction for a Legendrian knot to be a slice of a concordance from the trivial Legendrian knot with maximal Thurston-Bennequin invariant to itself. This allows to obstruct concordances from the Pretzel knot P(3,-3,-m) when m > 3 to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance.
Keywords
Cite
@article{arxiv.2207.02752,
title = {Doubly slice knots and obstruction to Lagrangian concordance},
author = {Baptiste Chantraine and Noémie Legout},
journal= {arXiv preprint arXiv:2207.02752},
year = {2023}
}
Comments
4 Pages, 1 Figure. v2: minor corrections, accepted for publication in "Comptes Rendus. Math\'ematique."