Dehn surgeries on strongly invertible knots which yield lens spaces

In this article we show no Dehn surgery on nontrivial strongly invertible knots can yield the lens space for any integer . In order to do that, we determine band attaches to -torus links producing the trivial knot.

     

Distance between toroidal surgeries on hyperbolic knots in the -sphere

For a hyperbolic knot in the -sphere, at most finitely many Dehn surgeries yield non-hyperbolic -manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed -manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal slope, is known to be integral or half-integral. We show that the distance between two integral toroidal slopes for a hyperbolic knot, except the figure-eight knot, is at most four.