Toroidal Surgeries on Hyperbolic Knots, II

For a hyperbolic knot K in S3, a toroidal surgery on K is integral or half-integral. In the previous paper, we proved that all integers occur among the toroidal slopes of hyperbolic knots. Hence there is no universal upper bound for toroidal slopes, generally. We propose an upper bound in terms of genera of knots, and we show that this is the case for two special but important classes, i.e., alternating knots and genus one knots