Journal of Symplectic Geometry

Volume 20 (2022)

Number 5

Contact $(+1)$-surgeries on rational homology $3$-spheres

Pages: 1037 – 1066



Fan Ding (School of Mathematical Sciences and LMAM, Peking University, Beijing, China)

Youlin Li (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China)

Zhongtao Wu (Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong)


In this paper, sufficient conditions for contact $(+1)$-surgeries along Legendrian knots in contact rational homology $3$-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact $(\pm 1)$-surgeries along Legendrian links in the standard contact $3$-sphere. We also obtain a sufficient condition for contact $(+1)$-surgeries along Legendrian twocomponent links in the standard contact $3$-sphere to be overtwisted via their front projections.

Received 12 November 2020

Accepted 19 February 2022

Published 24 April 2023