Hyperbolic Knots with distance-3 Toroidal Surgeries in S³

Hyperbolic Knots with distance-3 Toroidal Surgeries in S³

Examples and Characterization

LAP Lambert Academic Publishing ( 2010-03-10 )

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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.

Book Details:

ISBN-13:

978-3-8383-5052-3

ISBN-10:

3838350529

EAN:

9783838350523

Book language:

English

By (author) :

César Garza
Luis Valdez-Sanchez

Number of pages:

64

Published on:

2010-03-10

Category:

Geometry