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arXiv · 2207.02752

Doubly slice knots and obstruction to Lagrangian concordance

Baptiste Chantraine·Noémie Legout
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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.

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Baptiste Chantraine, Noémie Legout. 2022-07-06. Doubly slice knots and obstruction to Lagrangian concordance. https://arxiv.org/abs/2207.02752

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