Discrete groups and computational geometry : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

Cooper, Haydn Mark

Discrete groups and computational geometry : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

dc.contributor.author	Cooper, Haydn Mark
dc.date.accessioned	2013-12-17T22:36:15Z
dc.date.available	2013-12-17T22:36:15Z
dc.date.issued	2013
dc.description.abstract	Let f and g be Möbius transformations with finite-orders p and q respectively. Further, let γ = tr[f; g] - 2, where tr[f; g] is the trace of the commutator of f and g in the standard SL(2;C) representation of Möbius transformations. The group G = hf; gi is then defined, up to conjugacy, by the parameter set (p; q; γ), whenever γ≠ 0. If the group G is discrete and non-elementary, then it is a Kleinian group. Kleinian groups are intimately related to hyperbolic 3-orbifolds. Here we develop a computer program that constructs a fundamental domain for such Kleinian groups. These constructions are undertaken directly from the parameters given above. We use this program to investigate, and add to, recent work on the classification of arithmetic Kleinian groups generated by two (finite-order) elliptic transformations.	en
dc.identifier.uri	http://hdl.handle.net/10179/4977
dc.language.iso	en	en
dc.publisher	Massey University	en_US
dc.rights	The Author	en_US
dc.subject	Möbius transformations	en
dc.subject	Kleinian groups	en
dc.subject	Computational geometry	en
dc.title	Discrete groups and computational geometry : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand	en
dc.type	Thesis	en
massey.contributor.author	Cooper, Haydn Mark	en
thesis.degree.discipline	Mathematics	en
thesis.degree.grantor	Massey University	en
thesis.degree.level	Doctoral	en
thesis.degree.name	Doctor of Philosophy (Ph.D.)	en