Hurwitz quaternion order and arithmetic Riemann surfaces

DOI10.1007/s10711-011-9582-3zbMath1339.11094arXivmath/0701137OpenAlexW2012365620MaRDI QIDQ715265

Mikhail G. Katz, Uzi Vishne, Mary Elizabeth Schaps

Publication date: 2 November 2012

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

Full work available at URL: https://arxiv.org/abs/math/0701137

zbMATH Keywords

Fuchsian groupsubgroup growthsystolehyperbolic reflection groupAzumaya algebrasquaternion algebrahyperbolic surfacearithmetic latticeHurwitz groupHurwitz order

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Finite-dimensional division rings (16K20) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (6)

Construction of hyperbolic Riemann surfaces with large systoles ⋮ Systolic length of triangular modular curves ⋮ Relative systoles of relative-essential 2-complexes ⋮ Hyperellipticity and systoles of Klein surfaces ⋮ Bolza Quaternion Order and Asymptotics of Systoles Along Congruence Subgroups ⋮ An inequality for length and volume in the complex projective plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Flat currents modulo \(p\) in metric spaces and filling radius inequalities
• Cayley form, comass, and triality isomorphisms
• Volumes of balls in large Riemannian manifolds
• Bi-Lipschitz approximation by finite-dimensional imbeddings
• The length of the second shortest geodesic
• Systolic invariants of groups and 2-complexes via Grushko decomposition
• Systolic inequalities and Massey products in simply-connected manifolds
• Small values of the Lusternik-Schnirelman category for manifolds
• On manifolds satisfying stable systolic inequalities
• On the systoliy geometry of Bieberbach manifolds
• Homological invariance for asymptotic invariants and systolic inequalities
• Systolic volume of homology classes
• Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
• Systolic inequalities and minimal hypersurfaces
• Asymptotic bounds for separating systoles on surfaces
• The homology systole of hyperbolic Riemann surfaces
• Stable systolic category of manifolds and the cup-length
• The length of a shortest geodesic loop at a point
• \(E_7\), Wirtinger inequalities, Cayley 4-form, and homotopy
• Construction of class fields and zeta functions of algebraic curves
• Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic
• A short proof of Gromov's filling inequality
• Bounding volume by systoles of 3-manifolds
• Filling inequalities do not depend on topology
• A LOCAL OPTIMAL DIASTOLIC INEQUALITY ON THE TWO-SPHERE
• A Panoramic View of Riemannian Geometry

This page was built for publication: Hurwitz quaternion order and arithmetic Riemann surfaces