A classification of \(\mathbb{R}\)-Fuchsian subgroups of Picard modular groups

DOI10.5802/cml.51zbMath1481.11044arXiv1707.00154OpenAlexW3113347021WikidataQ109747343 ScholiaQ109747343MaRDI QIDQ2074017

Frédéric Paulin, Jouni Parkkonen

Publication date: 4 February 2022

Published in: Confluentes Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.00154

zbMATH Keywords

Heisenberg groupquaternion algebrahypersphereball quotientarithmetic Fuchsian groupscomplex hyperbolic geometryPicard modular group\(\mathbb{R}\)-circle

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Counting and equidistribution in Heisenberg groups
• Arithmetic subgroups of algebraic groups
• Prescribing the behaviour of geodesics in negative curvature
• Arithmétique des algèbres de quaternions
• A characterization of arithmetic Fuchsian groups
• Negative curves of small genus on surfaces
• Bounded negativity of self-intersection numbers of Shimura curves in Shimura surfaces
• Volumes of Picard modular surfaces
• Geodesic curves on Shimura surfaces
• TRACES IN COMPLEX HYPERBOLIC GEOMETRY
• A classification of $\mathbb{C}$-Fuchsian subgroups of Picard modular groups
• Density and maximality of arithmetic subgroups.
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)

This page was built for publication: A classification of \(\mathbb{R}\)-Fuchsian subgroups of Picard modular groups