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Distance between toroidal surgeries on hyperbolic knots in the -sphere
Authors:Masakazu Teragaito
Institution:Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
Abstract:For a hyperbolic knot in the $3$-sphere, at most finitely many Dehn surgeries yield non-hyperbolic $3$-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed $3$-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.

Keywords:Dehn surgery  toroidal surgery  knot
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