Lagrangian Approximation of Totally Real Concordances

Abstract

We show that a two-dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four-dimensional symplectiations, as well as of knotted Lagrangian tori in symplectisations of overtwisted contact three-manifolds.