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Jørgensen's inequality for metric spaces with application to the octonions
-
Sarah Markham
and
John R Parker
Published/Copyright:
February 16, 2007
Abstract
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.
Received: 2005-05-10
Published Online: 2007-02-16
Published in Print: 2007-01-26
© Walter de Gruyter 2007
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- The ovoidal hyperplanes of a dual polar space of rank 4
- Jørgensen's inequality for metric spaces with application to the octonions
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- On twisted tensor product group embeddings and the spin representation of symplectic groups
- Projective ovoids and generalized quadrangles
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Articles in the same Issue
- The ovoidal hyperplanes of a dual polar space of rank 4
- Jørgensen's inequality for metric spaces with application to the octonions
- On multiple blocking sets in Galois planes
- On twisted tensor product group embeddings and the spin representation of symplectic groups
- Projective ovoids and generalized quadrangles
- Multiple farthest points on Alexandrov surfaces
- Stiefel—Whitney classes for coherent real analytic sheaves
- On Weddle surfaces and their moduli
- Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature
