A classification of -Fuchsian subgroups of Picard modular groups
Confluentes Mathematici, Tome 10 (2018) no. 2, pp. 75-92.

Given an imaginary quadratic extension K of , we classify the maximal nonelementary subgroups of the Picard modular group PU(1,2;𝒪 K ) preserving a totally real totally geodesic plane in the complex hyperbolic plane 2 . We prove that these maximal -Fuchsian subgroups are arithmetic, and describe the quaternion algebras from which they arise. For instance, if the radius Δ of the corresponding -circle lies in -{0}, then the stabiliser arises from the quaternion algebra Δ,|D K | . We thus prove the existence of infinitely many orbits of K-arithmetic -circles in the hypersphere of 2 ().

Reçu le : 2018-12-01
Révisé le : 2018-09-02
Accepté le : 2018-12-02
Publié le : 2019-03-04
DOI : https://doi.org/10.5802/cml.51
Classification : 11F06,  11R52,  20H10,  20G20,  53C17,  53C55
Mots clés: Picard modular group, ball quotient, arithmetic Fuchsian groups, Heisenberg group, quaternion algebra, complex hyperbolic geometry, -circle, hypersphere
     author = {Jouni Parkkonen and Fr\'ed\'eric Paulin},
     title = {A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {10},
     number = {2},
     year = {2018},
     pages = {75-92},
     doi = {10.5802/cml.51},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2018__10_2_75_0/}
Parkkonen, Jouni; Paulin, Frédéric. A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups. Confluentes Mathematici, Tome 10 (2018) no. 2, pp. 75-92. doi : 10.5802/cml.51. https://cml.centre-mersenne.org/item/CML_2018__10_2_75_0/

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