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Sarah Markham, John R Parker

Jørgensen's inequality for metric spaces with application to the octonions

Jørgensen's inequality gives a necessary condition for the discreteness of a non-elementary group of isometries of hyperbolic 3-space. The main idea of the proof may be generalised widely but the statement is quite specialised. Here we give a scheme for restating Jørgensen's inequality for Möbius transformations of a metric space. This unifies many previously published versions of Jørgensen's inequality. We then show how this scheme may be applied by giving a version of Jørgensen's inequality for the octonionic hyperbolic plane.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 7, 01/2007
Pages: 19 - 38

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