Date of Degree

6-2017

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Abhijit Champanerkar

Committee Members

Walter Neumann

Ilya Kofman

Martin Bendersky

Subject Categories

Geometry and Topology

Keywords

Hyerbolic 3-manifolds, Knot theory, Geometric Topology, Link diagrams, Fully Augmented Links

Abstract

We study the geometry of fully augmented link complements in the 3-sphere by looking at their link diagrams. We extend the method introduced by Thistlethwaite and Tsvietkova to fully augmented links and define a system of algebraic equations in terms of parameters coming from edges and crossings of the link diagrams. Combining it with the work of Purcell, we show that the solutions to these algebraic equations are related to the cusp shapes of fully augmented link complements. As an application we use the cusp shapes to study the commensurability classes of fully augmented links.

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