Non-decomposable Lagrangian endoconcordances and Khovanov homology

Abstract

In this note, we construct non-decomposable Lagrangian endoconcordances of Legendrian knots. We prove that for any positive integer k, there exist a (stabilised) Legendrian knot and a Lagrangian fillable Legendrian knot in the standard contact 3-sphere, each admitting at least k pairwise Hamiltonian non-isotopic relative boundary, non-decomposable Lagrangian endoconcordances. The obstruction to decomposability that we rely on is based on Khovanov homology.