Exact Lagrangian caps of Legendrian knots

Abstract

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 show this, we construct a family combinatorial moves on knot projections with some additional data that correspond to Lagrangian cobordisms between knots.

22 pages, 25 figures

References in corpus (1)

• Exact Lagrangian caps and non-uniruled Lagrangian submanifolds

Cited by in corpus (1)

• Exact Lagrangian caps and non-uniruled Lagrangian submanifolds