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On the discreteness of Möbius groups in all dimensions
Published online by Cambridge University Press: 21 April 2004
Abstract
We show that a non-elementary Möbius group acting in higher dimensions is discrete if and only if its elementary subgroup whose elements fix every limit point is finite and every two-generator subgroup is discrete. This result gives an improvement over earlier results of Abikoff and Haas [1], Fang and Nai [5], Martin [11] and the author [9]. We also give an example to show that the first condition is necessary when dimension $n\ge 3$.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 3 , May 2004 , pp. 547 - 555
- Copyright
- 2004 Cambridge Philosophical Society
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