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Flexing closed hyperbolic
manifolds
D Cooper, D D Long and M B Thistlethwaite |
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Geometry & Topology 11 (2007) 2413–2440
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Abstract |
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We show that for certain closed hyperbolic manifolds, one can nontrivially deform the real hyperbolic structure when it is considered as a real projective structure. It is also shown that in the presence of a mild smoothness hypothesis, the existence of such real projective deformations is equivalent to the question of whether one can nontrivially deform the canonical representation of the real hyperbolic structure when it is considered as a group of complex hyperbolic isometries. The set of closed hyperbolic manifolds for which one can do this seems mysterious. |
Keywords
real projective structure, complex isometry, flexing
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Mathematical Subject Classification 2000
Primary: 57M50
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References |
Forward citations |
Publication
Received: 18 December 2006
Accepted: 3 September 2007
Published: 17 December 2007
Proposed: Walter Neumann
Seconded: Dave Gabai, Martin Bridson
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Authors |
| D Cooper | |
| Department of Mathematics University of California Santa Barbara CA 93106 USA |
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| D D Long | |
| Department of Mathematics University of California Santa Barbara CA 93106 USA |
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| M B Thistlethwaite | |
| Department of Mathematics University of Tennessee Knoxville TN 37996 USA |
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