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Basic \(\mathop {\mathrm {PU}}(1,1)\)-representations of the hyperelliptic group are discrete

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Abstract

We show that a \(\mathop {\mathrm {PU}}(1,1)\)-representation of the hyperelliptic group \(H_n\) is basic if and only if it is discrete and faithful, thus partially proving a conjecture by S. Anan’in (A hyperelliptic view on Teichmuller space. II, 2009. arXiv:0709.1711) and S. Anan’in and E. Bento Gonçalves (A hyperelliptic view on Teichmuller space. I, 2007. arXiv:0907.1633) in the case of the Poincaré disc.

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  1. Departamento de Matemática, ICMC, Universidade de São Paulo, São Carlos, Brasil

    Felipe A. Franco

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  1. Felipe A. Franco
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Franco, F.A. Basic \(\mathop {\mathrm {PU}}(1,1)\)-representations of the hyperelliptic group are discrete. Geom Dedicata 216, 13 (2022). https://doi.org/10.1007/s10711-022-00678-7

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