The simplest hyperbolic knots with non-integral toroidal surgery

摘要

For a hyperbolic knot K in S~3, a toroidal surgery on K is integral or half-integral. It is well known that no 2-bridge knot admits non-integral toroidal surgery. In this paper, we show that the (-2, 3, 7)-pretzel knot and its mirror image are the only 3-bridge knots that admit non-integral toroidal surgery.