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Full-Text Articles in Other Mathematics
A Stronger Strong Schottky Lemma For Euclidean Buildings, Michael E. Ferguson
A Stronger Strong Schottky Lemma For Euclidean Buildings, Michael E. Ferguson
Dissertations, Theses, and Capstone Projects
We provide a criterion for two hyperbolic isometries of a Euclidean building to generate a free group of rank two. In particular, we extend the application of a Strong Schottky Lemma to buildings given by Alperin, Farb and Noskov. We then use this extension to obtain an infinite family of matrices that generate a free group of rank two. In doing so, we also introduce an algorithm that terminates in finite time if the lemma is applicable for pairs of certain kinds of matrices acting on the Euclidean building for the special linear group over certain discretely valued fields.
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Van Kampen Diagrams And Small Cancellation Theory, Kelsey N. Lowrey
Master's Theses
Cocompact Cubulations Of Mixed 3-Manifolds, Joseph Dixon Tidmore
Cocompact Cubulations Of Mixed 3-Manifolds, Joseph Dixon Tidmore
Theses and Dissertations
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.