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2022 Projections in Moduli Spaces of the Kleinian Groups
Hala Alaqad, Jianhua Gong, Gaven Martin
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Abstr. Appl. Anal. 2022: 1-10 (2022). DOI: 10.1155/2022/6311193

Abstract

A two-generator Kleinian group f,g can be naturally associated with a discrete group f,ϕ with the generator ϕ of order two and where f,ϕfϕ-1=f,gfg-1f,g,f,ϕ: f,gfg-1=2 This is useful in studying the geometry of the Kleinian groups since f,g will be discrete only if f,ϕ is, and the moduli space of groups f,ϕ is one complex dimension less. This gives a necessary condition in a simpler space to determine the discreteness of f,g. The dimension reduction here is realised by a projection of principal characters of the two-generator Kleinian groups. In applications, it is important to know that the image of the moduli space of Kleinian groups under this projection is closed and, among other results, we show how this follows from Jørgensen’s results on algebraic convergence.

Acknowledgments

This research is supported by UAEU UPAR Grant (31S315). This paper is partly contained in the first author’s Ph.D. thesis.

Citation

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Hala Alaqad. Jianhua Gong. Gaven Martin. "Projections in Moduli Spaces of the Kleinian Groups." Abstr. Appl. Anal. 2022 1 - 10, 2022. https://doi.org/10.1155/2022/6311193

Information

Received: 11 September 2021; Accepted: 6 April 2022; Published: 2022
First available in Project Euclid: 28 July 2022

Digital Object Identifier: 10.1155/2022/6311193

Rights: Copyright © 2022 Hindawi

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