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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

Let 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.

Identiferoai:union.ndltd.org:ADTP/243162
Date January 2008
CreatorsCooper, Haydn
PublisherMassey University
Source SetsAustraliasian Digital Theses Program
LanguageEnglish
Detected LanguageEnglish

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