Exact Lagrangian caps of Legendrian knots

We prove that any Legendrian knot in $(S^3,ξ_{std})$ bounds an exact Lagrangian surface in $\mathbb{R}^4\setminus B^4$ after a sufficient number of stabilizations. In order to show this, we construct a family combinatorial moves on knot projections with some additional data that correspond to Lagrangian cobordisms between knots.

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