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From the hyperbolic
$24$–cell to the cuboctahedron
Steven P Kerckhoff and Peter A Storm |
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Geometry & Topology 14 (2010) 1383–1477
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Abstract |
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We describe a family of –dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic –cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of . It also leads to finite covolume Coxeter groups which are the homomorphic image of the group of reflections in the hyperbolic –cell. The examples are constructed very explicitly, both from an algebraic and a geometric point of view. The method used can be viewed as a –dimensional, but infinite volume, analog of –dimensional hyperbolic Dehn filling. |
Keywords
hyperbolic manifold, discrete group
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Mathematical Subject Classification 2000
Primary: 22E40
Secondary: 20F55, 20H10, 51M99
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References |
Publication
Received: 25 August 2008
Revised: 18 May 2010
Accepted: 22 March 2010
Published: 7 June 2010
Proposed: Benson Farb
Seconded: Walter Neumann, Jean-Pierre Otal
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Authors |
| Steven P Kerckhoff | |
| Department of Mathematics Stanford University Building 380, Sloan Hall Stanford, CA 94305 USA |
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| Peter A Storm | |
| Jane Street Capital, LLC 1 New York Plaza, 33rd Floor New York, NY 10004 USA |
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