Obstructions to Lagrangian concordance

Abstract

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in ${ℝ}^3$. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with nonreversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to $14$ crossings that have Legendrian representatives that are Lagrangian slice.