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http://hdl.handle.net/11375/20263
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DC Field | Value | Language |
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dc.contributor.advisor | Hambleton, Ian | - |
dc.contributor.author | Kairzhan, Adilbek | - |
dc.date.accessioned | 2016-08-30T13:55:52Z | - |
dc.date.available | 2016-08-30T13:55:52Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | http://hdl.handle.net/11375/20263 | - |
dc.description.abstract | 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. | en_US |
dc.language.iso | en | en_US |
dc.subject | group actions | en_US |
dc.subject | topological conjugacy | en_US |
dc.subject | convergence groups | en_US |
dc.subject | pseudo-Riemannian space forms | en_US |
dc.subject | compactification of actions | en_US |
dc.title | Infinite discrete group actions | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | Mathematics and Statistics | en_US |
dc.description.degreetype | Thesis | en_US |
dc.description.degree | Master of Science (MSc) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Kairzhan_Adilbek_2016August_MSc.pdf | thesis pdf file | 489.16 kB | Adobe PDF | View/Open |
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