Stein fillings of contact 3-manifolds obtained as Legendrian surgeries

Abstract

In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on $(S^3,{\xi }_{std})$ along certain Legendrian 2-bridge knots. We also classify Stein fillings, up to symplectic deformation, of an infinite family of contact 3-manifolds which can be obtained by Legendrian surgeries on $(S^3,{\xi }_{std})$ along certain Legendrian twist knots. As a corollary, we obtain a classification of Stein fillings of an infinite family of contact hyperbolic 3-manifolds up to symplectic deformation.

Made changes to reflect referee comments. Proofs of some of the key lemmas are expanded. Final version accepted in Journal of Symplectic Geometry

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Stein fillings of planar open books
• Symplectic fillings of Seifert fibered spaces

Cited by in corpus (4)

• Calabi-Yau Caps, Uniruled Caps and Symplectic Fillings
• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• Partial twists and exotic Stein fillings
• Stein fillings of homology $3$-spheres and mapping class groups