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The moduli space of the modular group in complex hyperbolic geometry

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Inventiones mathematicae Aims and scope

Abstract.

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 ℂ-spheres of Falbel-Zocca are related to the ℝ-spheres (hybrid spheres) of Schwartz.

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Authors and Affiliations

  1. Institut de Mathématiques, Université Pierre et Marie Curie, 4, place Jussieu, F-75252 Paris, France (e-mail: falbel@math.jussieu.fr), , , , , , FR

    Elisha Falbel

  2. Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, England (e-mail: J.R.Parker@durham.ac.uk), , , , , , GB

    John R. Parker

Authors
  1. Elisha Falbel
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  2. John R. Parker
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Additional information

Oblatum 16-X-2001 & 12-VIII-2002¶Published online: 8 November 2002

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ID="*"This research was partially supported by an Alliance grant from the British Council and EGIDE

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Falbel, E., Parker, J. The moduli space of the modular group in complex hyperbolic geometry. Invent. math. 152, 57–88 (2003). https://doi.org/10.1007/s00222-002-0267-2

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  • DOI: https://doi.org/10.1007/s00222-002-0267-2

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