Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Stein fillings of contact 3-manifolds obtained as Legendrian surgeries

Pages: 119 – 147

DOI: http://dx.doi.org/10.4310/JSG.2016.v14.n1.a5

Authors

Amey Kaloti (School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Youlin Li (Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China)

Abstract

In this paper, 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.

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Published 24 June 2016