Lens space surgeries and a conjecture of Goda and Teragaito

Abstract

Using work of Ozsváth and Szabó, we show that if a nontrivial knot in $S^3$ admits a lens space surgery with slope $p$, then $p\le 4g+3$, where $g$ is the genus of the knot. This is a close approximation to a bound conjectured by Goda and Teragaito.