Non-regular Lagrangian concordances between Lagrangian fillable Legendrian knots

Abstract

In this short note, we construct a family of non-regular, and therefore non-decomposable, Lagrangian concordances between Lagrangian fillable Legendrian knots in the standard contact 3-dimensional sphere. More precisely, for every decomposable Lagrangian concordance from ${\Lambda }_{-}$ to ${\Lambda }_{+}$, where ${\Lambda }_{\pm }$ are smoothly non-isotopic Legendrian knots, we construct a non-regular Lagrangian concordance from ${\Lambda }_{+}^{\prime }$ to ${\Lambda }_{-}^{\prime }$, where both ${\Lambda }_{\pm }^{\prime }$ are Lagrangian fillable Legendrian knots obtained from ${\Lambda }_{\pm }$ by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations.

11 pages, 5 figures; minor revision; it has been accepted for publication in the Proceedings of the American Mathematical Society