Symplectic Fillings, Contact Surgeries, and Lagrangian Disks.

This paper completely answers the question of when contact |$(r)$| –surgery on a Legendrian knot in the standard contact structure on |$S^3$| yields a symplectically fillable contact manifold for |$r\in (0,1]$|⁠. We also give obstructions for other positive |$r$| and investigate Lagrangian fillings of Legendrian knots. [ABSTRACT FROM AUTHOR]