Dissertations, Theses, and Capstone Projects
Date of Degree
2-2023
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Khalid Bou-Rabee
Committee Members
Ara Basmajian
Benjamin Steinberg
Subject Categories
Algebra | Discrete Mathematics and Combinatorics | Geometry and Topology | Other Mathematics
Keywords
Free Groups, Euclidean Buildings, Geometric Group Theory, Strong Schottky Lemma
Abstract
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.
Recommended Citation
Ferguson, Michael E., "A Stronger Strong Schottky Lemma for Euclidean Buildings" (2023). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/5187
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons, Other Mathematics Commons