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ISSN 1088-6850(e) ISSN 0002-9947(p)

Distance between toroidal surgeries on hyperbolic knots in the -sphere

Author: Masakazu Teragaito
Journal: Trans. Amer. Math. Soc. 358 (2006), 1051-1075
MSC (2000): Primary 57M25
Posted: April 13, 2005
Erratum: Trans. Amer. Math. Soc. 361 (2009), 3373-3374.
Correction: Trans. Amer. Math. Soc. 272 (1982), 803-807.
MathSciNet review: 2187645
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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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