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

Abstract

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.