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The moduli space of the modular group in complex hyperbolic geometry.

Falbel, E. and Parker, J. R. (2003) 'The moduli space of the modular group in complex hyperbolic geometry.', Inventiones mathematicae., 152 (1). pp. 57-88.


We construct the space of discrete, faithful, type-preserving representations of the modular group into the isometry group of complex hyperbolic 2-space up to conjugacy. This is the first Fuchsian group for which the entire complex hyperbolic deformation space has been constructed. We also show how the ³-spheres of Falbel-Zocca are related to the Â-spheres (hybrid spheres) of Schwartz.

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Date of first online publication:April 2003
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