Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Exact Lagrangian caps of Legendrian knots

Pages: 269 – 295



Francesco Lin (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.)


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.

Published 24 June 2016