Using Twisted Alexander Polynomials to Detect Fiberability

The purpose of this dissertation is to discuss how certain algebraic invariants of 3-manifolds, the twisted Alexander polynomials, can be effectively used in the study of fiberability and the Thurston norm of links. The links to which we have applied this technique belong to the class of graph links. For graph links, D. Eisenbud and W. Neumann introduced splice diagrams and developed a method to use the combinatorial informationincluded in splice diagrams to determine berability and the Thurston norm]. We use twisted Alexander polynomials to prove that the exterior of a certain graph knot, whose splice diagram is given, is not fibered. Then we consider three 2-component graph links built out of this knot. For these links we use the same technique, involving twisted Alexanderpolynomials, to discuss their berability and Thurston norm. This allows us to demonstrate the effectiveness of twisted Alexander polynomials in this context (links in homology spheres different from S3), where no calculations exist in the literature