Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487356
Title: On the structure of Homeomorphism Groups
Author: Giblin, James Andrew
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2007
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Abstract:
We will prove four results concerning the structure of homeomorphism groups for manifolds. The first shows that the groups Qc(§n) and LIP(§n) of orientation preserving quasiconformal and bilipschitz homeomorphisms of §n respectively, are simple in dimensions 2 and above. The second and third prove classification results for transitive circle groups and transitive homeomorphism groups of lR respectively. The fourth shows that the Mapping class group of an orientable, closed (compact and without boundary), genus g > 5 surface cannot be realised by homeomorphisms. In the first c~apter we introduce some notation and terminology, and then go on to discuss the homeomorphism groups that we will be interested in. These are the groups of quasiconformal and bilipschitz homeomorphisms, Mobius transformations for both the sphere and the ball in all dimensions and convergence groups. The later chapters deal with one of our main results each. We give a brief introduction to each before presenting their proofs. Chapter 2 shows that Qc(§n) and LIP(§n) are simple in dimensions 2 and above. Chapters 3 and 4 prove the classification results for circle groups and homeomorphism groups of R Finally, Chapter 5 shows that the Mapping class group of an orientable, closed, genus g ~ 5 surface cannot be realised by homeomorphisms.
Supervisor: Not available Sponsor: Not available
Qualification Name: University of Warwick, 2007 Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.487356  DOI: Not available
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