Exact Lagrangian caps of Legendrian knots

We prove that any Legendrian knot in $(S^3, \xi_{std})$ bounds an exact Lagrangian surface in $\mathbb{R}^4 \setminus B^4$ 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.

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Published 24 June 2016