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Topics in hyperbolic groups
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Billington, Stephen (1999) Topics in hyperbolic groups. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3252892~S15
Abstract
Hyperbolic groups are a class of groups introduced by Gromov in 1987, which form an important part of geometric group theory. In Chapter 1, we give an introduction to this subject.
In Chapter 2, we use the theory of complexes of groups to show that the integral homology and cohomology groups of a hyperbolic group are computable by a Turing machine.
In Chapter 3, we present the boundary of a hyperbolic group as an inverse limit of topological spaces and use this to give computable estimates for properties of the boundary.
In Chapter 4, we investigate symbolic dynamic properties concerning hyperbolic groups. In paricular, we give symbolic codings for the actions on the boundary of a hyperbolic and actions on the geodesic flow on a hyperbolic group.
In Chapter 5 we investigate the problem of determining when graphs are Cayley graphs. The graphs which we are concerned with are regular and semi-regular planar graphs.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Hyperbolic groups, Turing machines, Homology theory, Symbolic dynamics, Cayley graphs | ||||
Official Date: | 28 August 1999 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Epstein, D. B. A. | ||||
Format of File: | |||||
Extent: | 167 leaves : illustrations | ||||
Language: | eng |
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