Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions

DOI10.1007/s10711-017-0288-zzbMath1447.20022arXiv1503.07214OpenAlexW2964158598MaRDI QIDQ684206

Fabio Vlacci, Alberto Verjovsky, Juan Pablo Díaz

Publication date: 9 February 2018

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07214

zbMATH Keywords

modular groups4-orbifoldsarithmetic hyperbolic 4-manifoldsquaternionic hyperbolic geometry

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Discontinuous groups of transformations (57S30) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Related Items (4)

Bianchi and Hilbert-Blumenthal quaternionic orbifolds ⋮ A direct approach to quaternionic manifolds ⋮ Presentations for cusped arithmetic hyperbolic lattices ⋮ A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

Cites Work

• Orientation preserving Möbius transformations in \(\mathbb{R}_\infty^4\) and quaternionic determinants
• The quaternion formalism for Möbius groups in four or fewer dimensions
• On the Euler number of an orbifold
• Quaternionic modular groups
• Quaternionic determinants
• Discrete groups generated by reflections
• Foundations of Hyperbolic Manifolds
• Higher Dimensional Analogues of the Modular and Picard Groups
• The Volume Spectrum of Hyperbolic 4-Manifolds
• Moebius transformations and the Poincare distance in the quaternionic setting
• Quaternions and Reflections
• Hyperbolic manifolds and discrete groups
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