Exceptional surgeries and genera of knots

Abstract

Let $K(r)$ be the 3-manifold obtained by a Dehn surgery on a hyperbolic knot $K$ in the 3-sphere a along a slope $r \ne \infty$. We show that if $|r| > 3 \cdot 2^{7/4} g$, then $K(r)$ is an irreducible 3-manifold with infinite and word-hyperbolic fundamental group, where $g$ denotes the genus of $K$.