Date of Award
2009-01-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Luis G. Valdez-Sánchez
Abstract
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 $\gcd(a,b) = 1$.
Language
en
Provenance
Received from ProQuest
Copyright Date
2009
File Size
64 pages
File Format
application/pdf
Rights Holder
Cesar Garza
Recommended Citation
Garza, Cesar, "Examples of hyperbolic knots with distance 3 toroidal surgeries in the 3-sphere" (2009). Open Access Theses & Dissertations. 262.
https://scholarworks.utep.edu/open_etd/262