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Title: Topics in hyperbolic groups
Author: Billington, Stephen
ISNI:       0000 0001 3464 2317
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1999
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics