Title
Hyperbolic Knots with distance3 Toroidal Surgeries in S: Examples and Characterization,Used
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By the work of Thurston, any surgery on a hyperbolic knot in the 3sphere produces a hyperbolic 3manifold except in at most finitely many cases. So far, the figure8 knot seems to be the best candidate for a hyperbolic knot with the most (8) nontrivial exceptional surgeries. In recent years, much progress has been made in the classification of hyperbolic knots admitting more than one exceptional toroidal surgery. In fact, such classification is known for toroidal surgeries with distance at least 4. We give a necessary condition for a hyperbolic knot in the 3sphere admitting two toroidal surgeries at distance 3, whose slopes are represented by twice punctured essential separating tori. Namely, such knots belong to a family K(a, b, n), where a, b, n are integers and gcd(a, b) = 1. This result should be specially useful for geometers, topologists or anyone else interested in the theory of 3dimensional manifolds.
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