The Hyperbolic Structure of the Complements of Rational Links with Conway Notation mn for m,n≥2
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 we note changes in the hyperbolic structure as half-twists are added to each of its com- ponent tangles. We model the complements of the links under investigation in a speci c way such that the following patterns are observed. Our model for the complement of a link with Conway notation mn, m, n ≥ 2, will contain (m + n) - 3 pairs of tetrahedra and 2((m + n) - 3) edge types. Furthermore, the tetrahedral con guration and edge equations corresponding to these models change in a predictable way as we each additional half-twist. The 2((m+ n)-3) edge equations are then simpli ed down to (m + n)- 3 equations and solved. Their solutions determine the hyperbolic structure and are used to determine the hyperbolic volume of each knot under investigation. As m and n increase, the growth rate of the hyperbolic volume decreases.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2011
- F&M Theses Collection 
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Dubicki, Sarah (2011)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 ...
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.