(1,1) L-space knots

Abstract

We characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space surgeries. We also recover a characterization of the Berge manifold amongst 1-bridge braid exteriors.

17 pages, 5 figures; v2: corrects minor errors, has a new figure (Figure 2). This is the version to appear in Compositio Mathematica