Date of Award

1-1-2023

Language

English

Document Type

Master's Thesis

Degree Name

Master of Arts (MA)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (iii, 18 pages)

Dissertation/Thesis Chair

Matthew Zaremsky

Committee Members

Marco Varisco, Michael Lesnick

Keywords

finiteness, geometric group theory, group theory, morse theory, Geometric group theory, Group theory, Morse theory

Subject Categories

Physical Sciences and Mathematics

Abstract

Familiar properties such as group generation and presentation share certain topological features, allowing one to define many grades of group finiteness. They might also be finite in stronger or weaker senses. Groups finite in some grade might not be in others, and one can yield groups which match a given finiteness profile; Morse functions can operate on simplicial complexes and other elementary structures to indicate, through a series of isomorphisms, how to discover restrictedly finite groups.

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