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

Cooper, Haydn2009-08-20NO_RESTRIC2009-08-202008http://hdl.handle.net/10179/973Let 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.enThe AuthorIsometriesThree manifoldMargulis constantFields of Research::230000 Mathematical Sciences::230100 Mathematics::230112 Topology and manifoldsTwo 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 ZealandThesisQ112158729https://www.wikidata.org/wiki/Q112158729