Hyperbolic Knots with distance-3 Toroidal Surgeries in S³

by César Garza, Luis Valdez-Sanchez

Overview

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 necessary condition for a hyperbolic knot in the 3-sphere 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 3-dimensional manifolds.

Product Details

ISBN-13:	9783838350523
Publisher:	LAP Lambert Academic Publishing
Publication date:	06/29/2010
Pages:	64
Product dimensions:	6.00(w) x 9.00(h) x 0.15(d)