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2006 Computing Varieties of Representations of Hyperbolic $3$-Manifolds into $\SLfR$
Daryl Cooper, Darren Long, Morwen Thistlethwaite
Experiment. Math. 15(3): 291-306 (2006).


The geometric structure on a closed orientable hyperbolic 3-manifold determines a discrete faithful representation $\rho$ of its fundamental group into $\mathrm{SO^{+}(3,1)}$, unique up to conjugacy. Although Mostow rigidity prohibits us from deforming $\rho$, we can try to deform the composition of $\rho$ with inclusion of $\mathrm{SO^{+}(3,1)}$ into a larger group. In this sense, we have found by exact computation a small number of closed manifolds in the Hodgson-Weeks census for which $\rho$ deforms into $\mathrm{SL(4,\mathbb R)}$, thus showing that the hyperbolic structure can be deformed in these cases to a real projective structure. In this paper we describe the method for computing these deformations, particular attention being given to the manifold Vol3.


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Daryl Cooper. Darren Long. Morwen Thistlethwaite. "Computing Varieties of Representations of Hyperbolic $3$-Manifolds into $\SLfR$." Experiment. Math. 15 (3) 291 - 306, 2006.


Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1117.57016
MathSciNet: MR2264468

Primary: 57M50
Secondary: 57-04

Keywords: algorithms , deformation of geometric structure , hyperbolic 3-manifolds

Rights: Copyright © 2006 A K Peters, Ltd.


Vol.15 • No. 3 • 2006
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