The Hyperbolic Structure of the Complements of Rational Links with Conway Notation mn for m,n≥2
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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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