Legendrian lens space surgeries

Abstract

We show that every tight contact structure on any of the lens spaces $L(n{s}^2-s+1,s^2)$ with $n\ge 2$, $s\ge 1$, 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.

16 pages, 8 figures