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dc.contributor.advisorBleak, Collin Patrick
dc.contributor.advisorQuick, M. R. (Martyn R.)
dc.contributor.authorKhalid, Nayab
dc.description.abstractWe develop a combinatorial framework that assists in finding natural infinite “geometric” presentations for a large subclass of rearrangement groups of fractals – defined by Belk and Forrest, namely rearrangement groups acting on F-type topological spaces. In this framework, for a given fractal set with its group of “rearrangements”, the group generators have a natural one-to-one correspondence with the standard basis of the fractal set, and the relations are all conjugacy relations. We use this framework to produce a presentation for Richard Thompson’s group F. This presentation has been mentioned before by Dehornoy, but a combinatorial method to find the length of an element in terms of the generating set of this presentation has been hitherto unknown. We provide algorithms that express an element of F in terms of our generating set and reduce a word representing the identity in F to the trivial word. We conjecture that this framework can be used to find infinite presentations for all groups in the subclass of rearrangement groups acting on F-type topological spaces.en_US
dc.description.sponsorship"I have been supported in this PhD by a Commonwealth Scholarship (PKCS-2015-496), funded by the UK Government."--Fundingen
dc.publisherUniversity of St Andrewsen
dc.titleRearrangement groups of connected spacesen_US
dc.contributor.sponsorCommonwealth Scholarship Commission in the United Kingdomen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US

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