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http://hdl.handle.net/11375/20263
Title: | Infinite discrete group actions |
Authors: | Kairzhan, Adilbek |
Advisor: | Hambleton, Ian |
Department: | Mathematics and Statistics |
Keywords: | group actions;topological conjugacy;convergence groups;pseudo-Riemannian space forms;compactification of actions |
Publication Date: | 2016 |
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. |
URI: | http://hdl.handle.net/11375/20263 |
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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