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15 July 2002 Local rigidity of hyperbolic 3-manifolds after Dehn surgery
Kevin P. Scannell
Duke Math. J. 114(1): 1-14 (15 July 2002). DOI: 10.1215/S0012-7094-02-11411-2

Abstract

It is well known that some lattices in ${\rm SO}(n,1)$ can be nontrivially deformed when included in ${\rm SO}(n+1,1)$ (e.g., via bending on a totally geodesic hypersurface); this contrasts with the (super) rigidity of higher rank lattices. M. Kapovich recently gave the first examples of lattices in ${\rm SO}(3,1)$ which are locally rigid in ${\rm SO}(4,1)$ by considering closed hyperbolic $3$-manifolds obtained by Dehn filling on hyperbolic two-bridge knots. We generalize this result to Dehn filling on a more general class of one-cusped finite volume hyperbolic $3$-manifolds, allowing us to produce the first examples of closed hyperbolic $3$-manifolds which contain embedded quasi-Fuchsian surfaces but are locally rigid in ${\rm SO}(4,1)$.

Citation

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Kevin P. Scannell. "Local rigidity of hyperbolic 3-manifolds after Dehn surgery." Duke Math. J. 114 (1) 1 - 14, 15 July 2002. https://doi.org/10.1215/S0012-7094-02-11411-2

Information

Published: 15 July 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1025.57019
MathSciNet: MR1915033
Digital Object Identifier: 10.1215/S0012-7094-02-11411-2

Subjects:
Primary: 57M50
Secondary: 22E40, 57N16

Rights: Copyright © 2002 Duke University Press

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Vol.114 • No. 1 • 15 July 2002
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