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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

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    Abstract
    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.
    Date
    2008
    Author
    Cooper, Haydn
    Rights
    The Author
    Publisher
    Massey University
    URI
    http://hdl.handle.net/10179/973
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