We prove that any Legendrian knot in (S3, ξstd) bounds an exact Lagrangian surface in ℝ4 \ B4 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.
|Original language||English (US)|
|Number of pages||27|
|Journal||Journal of Symplectic Geometry|
|State||Published - Jan 1 2016|
All Science Journal Classification (ASJC) codes
- Geometry and Topology