Hyperbolic Knots with distance-3 Toroidal Surgeries in S³ - Garza, César;Valdez-Sanchez, Luis
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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…mehr

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Produktbeschreibung
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.
Autorenporträt
César Garza is a Teaching Assistant at the University of Texas, where he pursues a Ph.D. in Math. He obtained his Masters degree in Mathematics from the University of Texas at El Paso and his Bachelors degree in Mechatronics from the Instituto Tecnológico y de Estudios Superiores de Monterrey. Luis Valdez-Sanchez is an associate professor at UTEP.