Year of Award

2017

Document Type

Dissertation

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Department or School/College

Department of Mathematical Sciences

Committee Chair

Eric Chesebro

Commitee Members

Kelly McKinnie, Karel Stroethoff, Nikolaus Vonessen, Nate McCrady

Publisher

University of Montana

Abstract

Culler-Shalen theory uses the algebraic geometry of a 3-manifold's SL2(C)-character variety to construct essential surfaces in the manifold. There are module structures associated to the coordinate ring of the character variety which are intimately related to essential surface construction. When these modules are finitely generated, we derive a formula for their rank that incorporates the variety's field of definition and the Culler-Shalen norm.

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© Copyright 2017 Charles Walter Katerba