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Home » GAAHD Research Seminar: On the classification of C-Fuchsian subgroups of Picard modular groups

Seminar

GAAHD Research Seminar: On the classification of C-Fuchsian subgroups of Picard modular groups April 21, 2015 (10:30 AM PDT - 12:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Frédéric Paulin (Université de Paris XI)
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Given an imaginary quadratic number field K, we give a classification of the maximal nonelementary subgroups of the Picard modular group PSU_{1,2}(O_K) preserving a complex geodesic in the complex hyperbolic plane. Complementing work of Holzapfel, Chinburg-Stover and Möller-Toledo, we show that these maximal C-Fuchsian subgroups are arithmetic, arising from a quaternion algebra over Q with Hilbert symbol (D,D_K) for some explicit positive integer D and with D_K the discriminant of K. We thus prove the existence of infinitely many orbits of K-arithmetic Cartan chains in Poincaré's hypersphere in the complex projective plane. This is a joint work with Jouni Parkkonen.

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