The moduli space of the modular group in complex hyperbolic geometry

Falbel, Elisha; Parker, John R.

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 ³-spheres of Falbel-Zocca are related to the Â-spheres (hybrid spheres) of Schwartz.

Citation

Falbel, E., & Parker, J. R. (2003). The moduli space of the modular group in complex hyperbolic geometry. Inventiones Mathematicae, 152(1), 57-88. https://doi.org/10.1007/s00222-002-0267-2

• Journal Article Type: Article
• Publication Date: 2003-04
• Deposit Date: Feb 29, 2008
• Journal: Inventiones Mathematicae
• Print ISSN: 0020-9910
• Electronic ISSN: 1432-1297
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 152
• Issue: 1
• Pages: 57-88
• DOI: https://doi.org/10.1007/s00222-002-0267-2
• Public URL: https://durham-repository.worktribe.com/output/1598831
• Publisher URL: http://www.springerlink.com/content/nnncv56ard4p2ahd/