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

	PDF WRAP_THESIS_Buckley_2010.pdf - Requires a PDF viewer. Download (762Kb)
	Other (Permission e-mail) Re__Placing_your_PhD_thesis_online.msg Embargoed item. Restricted access to Repository staff only Download (26Kb)

Request Changes to record.

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 (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Hyperbolic groups, Conjugacy classes, Cayley graphs
Official Date:	June 2010
Dates:	Date Event June 2010 Submitted
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Publication Status:	Unpublished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

Request changes or add full text files to a record

Repository staff actions (login required)

View Item