Examples of hyperbolic knots with distance 3 toroidal surgeries in the S3
By the work of Thurston, any surgery on a hyperbolic knot in the 3-sphere produces a hyperbolic 3-manifold except in at most finitely many cases. So far, the figure-8 knot seems to be the best candidate for a hyperbolic knot with the most (8) non-trivial 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 classification of hyperbolic knots in S 3 admitting two toroidal surgeries at distance 3, whose slopes are represented by twice punctured essential separating tori. Such knots belong to a family K(a, b, n), where a, b, n are integers and gcd(a, b) = 1. ^
Garza, Cesar, "Examples of hyperbolic knots with distance 3 toroidal surgeries in the S3" (2009). ETD Collection for University of Texas, El Paso. AAI1465251.