Non-decomposable cobordisms via Lagrangian moves

Abstract: We establish the use of Lagrangian diagram moves to build Lagrangian cobordisms of Legendrian knots. We then apply the moves to explore how to invert decomposable cobordisms, after adding some stabilizations. This is done by use of Reidemeister moves and handle attachments in the Lagrangian projection. As an application, we show an explicit construction of a Lagrangian concordance from a stabilized $m(9_{46})$ Legendrian knot to a stabilized unknot, i.e. a non-decomposable Lagrangian concordance of nonempty knots.