Legendrian Lens space surgeries (Q1654431)

The question which knots admit lens spaces surgeries is still open. The converse question (which lens spaces can be obtained by a single surgery on the 3-sphere) is trivial in a topological context. In this note, the authors discuss this converse question for contact manifolds: Which tight contact structures on a given lens space can be obtained by a Legendrian surgery along a Legendrian knot in \(S^3\) with some contact structure? The answer is the main result of the paper (Theorem 1.1).