Legendrian Lens Space Surgeries

Abstract

We show that every tight contact structure on any of the lens spaces $L(ns^2 - s + 1,s^2)$ with $n\geq 2, s \geq 1$, can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative torus knot $T(s, -(sn - 1))$ in the tight or an overtwisted contact structure on the 3-sphere.