Hyperbolic 3-Manifolds: Dehn Surgery Approach to the Figure-Eight Knot Complement
This project provides an examination of knot complements and their relationship to hyperbolic 3-manifolds. It begins with the study of knot theory, specifically knot complements in S. The knots we will be focusing on are those whose complements are hyperbolic, which includes a class of knots known as the twist knots, and in particular we will look at the hyperbolic structure of the link complement for the first even twist knot, the figure-eight knot. We then take the Dehn surgery approach to obtaining the structure of the figure-eight knot complement. By performing Dehn surgery on the Whitehead link, we are able to obtain the figure-eight knot. This project concludes by examining the Dehn surgery on the Whitehead link that yields the figure-eight knot. The performance of Dehn surgery on the hyperbolic structure of the Whitehead link leads us to the hyperbolic structure of the figure-eight knot complement.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2011
- F&M Theses Collection 
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Surma, Mark (2011)We use a specific application of Adams algorithm to investigate the hyper- bolic structure of rational links composed of two tangles. The investigation begins with the gure-eight knot (the simplest hyperbolic knot), and ...
P. W. W. (1828)Drawing of a castle with title "Square Root", dated February 7, 1828. Signed "by P.W.W." Contains mathematical calculations. From a scrapbook of drawings by unknown artist.