Description
An ongoing problem for the study of Coxeter polyhedra is the classification and construction of such polyhedra in a hyperbolic setting be they finite volume, compact, or otherwise. Within this setting, Coxeter groups may be represented as isometry groups acting on n-dimensional Lobachevsky space. This understanding differs significantly from the purely algebraic study of hyperbolicity for a Coxeter group, where the more varied conditions for parallel hyperplanes are suppressed in the group's presentation. Yet, in many cases, multiple polyhedra can be realized as the fundamental domain for a single Coxeter group up to isometry. This dissertation specifically investigates the formation of Coxeter polytopes with multiple parallel facets, relating the polytope's hyperbolicity to the eigen-structures and index of the polytope's gram matrix. This relation may be further computed through basic computational tools such as MATLAB.
Details
Title
- Hyperbolic Coxeter Polytopes with Multiple Infinity Edges
Contributors
- Doi, Philip Stephen (Author)
- Pauper, Julien (Thesis advisor)
- Fishel, Susanna (Committee member)
- Kotschwar, Brett (Committee member)
- Kawski, Matthias (Committee member)
- Childress, Nancy (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2024
Subjects
Resource Type
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Note
- Partial requirement for: Ph.D., Arizona State University, 2024
- Field of study: Mathematics