Asynchronous automaticity and products of hyperbolic spaces
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Jenny Beck (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Talia Fernos
Abstract: The main result of this thesis is a general procedure for constructing an asynchronous automatic structure for some finitely generated groups quasi-isometric to products of non-elementary hyperbolic spaces. An asynchronous automatic structure, in turn, can be used to represent the group computationally, by now-classical means which we describe in some detail. We refer to the structures at the heart of this procedure as factor-language systems, and give certain criteria which guarantee their existence. The particular criteria we describe enjoy an intriguing analogy with certain criteria of discreteness and reducibility in the theory of lattices in products of trees. Along the way, we explore the geometry of path systems, finite-state automata, regular languages, automatic relations, hyperbolic geometry, quasi-isometries, and HNN-extensions.
Asynchronous automaticity and products of hyperbolic spaces
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Created on 8/1/2024
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Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2024
- Keywords
- Algorithmic Group Theory, Automatic Group, Geometric Group Theory, Geometry, Group Theory, Hyperbolic Space