Two generator discrete groups of isometries and their representation : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand

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dc.contributor.authorCooper, Haydn
dc.date.accessioned2009-08-20T02:16:07Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2009-08-20T02:16:07Z
dc.date.issued2008
dc.description.abstractLet M Φ and Mψ be elements of PSL(2,C) representing orientation preserving isometries on the upper half-space model of hyperbolic 3-space Φ and ψ respectively. The parameters β = tr2(M Φ) - 4, β1 = tr2(Mψ) - 4, γ = tr[M Φ,Mψ] - 2, determine the discrete group (Φ ,ψ) uniquely up to conjugacy whenever γ ≠ 0. This thesis is concerned with explicitly lifting this parameterisation of (Φ , ψ) to PSO(1, 3) realised as a discrete 2 generator subgroup of orientation preserving isometries on the hyperboloid model of hyperbolic 3-space. We particularly focus on the case where both Φ and ψ are elliptic.en_US
dc.identifier.urihttp://hdl.handle.net/10179/973
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectIsometriesen_US
dc.subjectThree manifolden_US
dc.subjectMargulis constanten_US
dc.subject.otherFields of Research::230000 Mathematical Sciences::230100 Mathematics::230112 Topology and manifoldsen_US
dc.titleTwo generator discrete groups of isometries and their representation : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorCooper, Haydn
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Science (M. Sc.)en_US
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