Buckley, David John (2010) Conjugacy and subgroups of word-hyperbolic groups. PhD thesis, University of Warwick.

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Abstract

This thesis describes a number of algorithms and properties relating to Gromov’s word-hyperbolic groups. A fuller outline of the thesis is given, and a number of basic concepts relating to metric spaces, hyperbolicity and automaticity are first briefly detailed in Chapter 1. Chapter 2 then details a solution to the conjugacy problem for lists of elements in a word-hyperbolic group which can be run in linear time; this is an improvement on a quadratic time algorithm for lists which contain an infinite order element. Chapter 3 provides a number of further results and algorithms which build upon this result to efficiently solve problems relating to quasiconvex subgroups of word-hyperbolic groups – specifically, the problem of testing if an element conjugates into a quasiconvex subgroup, and testing equality of double cosets. In Chapter 4, a number of properties of certain coset Cayley graphs are studied, in particular showing that graph morphisms which preserve edge labels and directions and map a quasiconvex subset to a single point also preserve a variety of other properties, for instance hyperbolicity. Finally, Chapter 5 gives a proof that all word-hyperbolic groups are 14-hyperbolic with respect to some generating set.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Hyperbolic groups, Conjugacy classes, Cayley graphs
Date:	June 2010
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Holt, Derek F.
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	viii, 122 p. : ill.
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/3631

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