Knot Too Big: The Volume Conjecture for Augmented Links

Abstract

The Volume Conjecture, first proposed by Murakami and Murakami [27], proposes an explicit relation between two knot invariants: the n-colored Jones polynomial of a knot k and its hyperbolic volume of its complement. While we have understanding of each of these invariants separately, their connection is difficult to understand. Therefore, much of the progress made towards proving the Volume Conjecture has been verification of specific knots or knot families. This thesis aims to shed light on the case of Fully Augmented Links.