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Special Elliptic Isometries, Relative \(\mathrm{SU}(2,1)\)-Character Varieties, and Bendings

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Abstract

We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative \(\mathrm{SU}(2,1)\)-character varieties of the quadruply punctured sphere are described and applied to the study of length 5 relations.

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Notes

  1. For example, the study of short relations between isometries in the complex hyperbolic plane plays an important role in the construction of complex hyperbolic disc bundles in [6] and in [5].

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Acknowledgements

We are very grateful to the anonymous referee whose careful suggestions have greatly improved the paper.

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Authors and Affiliations

  1. Departamento de Matemática, IMECC, Universidade Estadual de Campinas, Campinas, Brazil

    Felipe A. Franco

  2. Departamento de Matemática, ICMC, Universidade de São Paulo, São Carlos, Brazil

    Carlos H. Grossi

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  1. Felipe A. Franco
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  2. Carlos H. Grossi
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Correspondence to Carlos H. Grossi.

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F. A. Franco: Supported by Grant 2014/00582-2, São Paulo Research Foundation (FAPESP), and by CNPq.

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Franco, F.A., Grossi, C.H. Special Elliptic Isometries, Relative \(\mathrm{SU}(2,1)\)-Character Varieties, and Bendings. J Geom Anal 31, 5988–6030 (2021). https://doi.org/10.1007/s12220-020-00512-0

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