The nature of this paper is expository. The purpose is to present the fundamental material concerning actions of infinite discrete groups on the n-sphere and pseudo-Riemannian space forms based on the works of Gehring, Martin and Kulkarni and provide appropriate examples. Actions on the n-sphere split it into ordinary and limit sets. Assuming, additionally, that a group acting on the n-sphere has a certain convergence property, this thesis includes conditions for the existence of a homeomorphism between the limit set and the set of Freudenthal ends, as well as topological and quasiconformal conjugacy between convergence and Mobius groups. Since the certain pseudo-Riemannian space forms are diffeomorphic to non-compact spaces, the work of Hambleton and Pedersen gives conditions for the extension of discrete co-compact group actions on pseudo-Riemannian space forms to actions on the sphere. An example of such an extension is described. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20263 |
| Date | January 2016 |
| Creators | Kairzhan, Adilbek |
| Contributors | Hambleton, Ian, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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