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 $\Lambda'_+$ to $\Lambda'_-$, where both $\Lambda'_\pm$ are Lagrangian fillable Legendrian knots obtained from $\Lambda_{\pm}$ by sufficiently many positive and negative stabilisations, followed by a sequence of Legendrian satellite operations.