Symplectic fillings, contact surgeries, and Lagrangian disks

Abstract

This paper completely answers the question of when contact (r)-surgery on a Legendrian knot in the standard contact structure on the 3-sphere 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.

arXiv comment23 pages, 8 figures. Improved exposition and changed claim relating decomposable and regular Lagrangians. This version to appear in IMRN