Exact Lagrangian caps of Legendrian knots

We prove that any Legendrian knot in (S-3, xi(std)) bounds an exact Lagrangian surface in R-4 \ B-4 after a sufficient number of stabilizations. In order to do this, we define Lagrangian projections, consisting of a knot projection along with some additional information, and construct a family of combinatorial moves which correspond to Lagrangian cobordisms between knots.