Abstract
In a series of papers, published in Mathematische Annalen, Bianchi and Blumenthal introduced the notions of Bianchi orbifolds and Hilbert-Blumnethal surfaces as generalizations of modular curves associated to quadratic fields. In this paper, in the same spirit, and following a similar line of reasoning, we introduce the concept of Bianchi and Hilbert–Blumenthal quaternionic orbifolds as generalizations of the Lipschitz and Hurwitz quaternionic modular orbifolds defined recently by Díaz, Vlacci, and the first author. In particular, we describe the cusp cross-sections of the Hilbert–Blumenthal quaternionic orbifolds in terms of fundamental units of real quadratic fields. These are 7-dimensional solvmanifolds which are virtual \(\mathbb {T}^6\) bundles over the circle with monodromy a linear Anosov diffeomorphism of the 6-torus.
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An extended version available in arXiv:1503.07214
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The first author was supported by grant IN108120, PAPIIT, DGAPA, Universidad Nacional Autónoma de México. The second author was supported by the CONACYT grant 432521, Estancias Posdoctorales por México 2021 - Modalidad Académica.
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Verjovsky, A., Zenteno, A. Bianchi and Hilbert–Blumenthal quaternionic orbifolds. Geom Dedicata 217, 108 (2023). https://doi.org/10.1007/s10711-023-00847-2
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DOI: https://doi.org/10.1007/s10711-023-00847-2