Date of Award

May 2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Chris Hruska

Committee Members

Craig Guilbault, Boris Okun, Rebecca Winarski, Allen Bell

Keywords

Chargeless, Geometric Group Theory, Geometric Topology, Mixed Manifold, Virtually Compact Special

Abstract

In this dissertation, we complete the classification of which compact 3-manifolds have a virtually compact special fundamental group by addressing the case of mixed 3-manifolds. A compact aspherical 3-manifold M is mixed if its JSJ decomposition has at least one JSJ torus and at least one hyperbolic block. We show the fundamental group of M is virtually compact special iff M is chargeless, i.e. each interior Seifert fibered block has a trivial Euler number relative to the fibers of adjacent blocks.

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