Distance between toroidal surgeries on hyperbolic knots in the -sphere |
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Authors: | Masakazu Teragaito |
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Institution: | Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524 |
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Abstract: | 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. |
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Keywords: | Dehn surgery toroidal surgery knot |
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