Doubly slice knots and obstruction to Lagrangian concordance

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 Lagrangian 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 $m\ge 4$ to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance.