The classification of discrete 2-generator subgroups of PSL(2,R)

DOI10.1007/BF02761412zbMath0497.20036MaRDI QIDQ1170629

J. Peter Matelski

Publication date: 1982

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

geometric algorithm2-generator Fuchsian groupsdiscreteness of 2-generator subgroups of PSL(2,R)

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Discrete subgroups of Lie groups (22E40) Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10)

Related Items (14)

Algorithms, complexity and discreteness criteria in \(PSL(2,C)\) ⋮ On Ford isometric spheres in complex hyperbolic space ⋮ A two-dimensional slice through the parameter space of two-generator Kleinian groups ⋮ A class of 2-generator subgroups of PSL(2,\({\mathbb{C}})\) ⋮ Discrete groups in three-dimensional Lobachevskij space generated by two rotations ⋮ Composition of subfactors : new examples of infinite depth subfactors ⋮ Hyperbolic cone-manifold structures with prescribed holonomy. I: Punctured tori ⋮ Discreteness criteria for \(\mathcal{RP}\) groups ⋮ Jörgensen’s inequality and purely loxodromic two-generator free Kleinian groups ⋮ The geometry of two generator groups: hyperelliptic handlebodies ⋮ The modular torus has maximal length spectrum ⋮ All generating pairs of all two-generator Fuchsian groups ⋮ The punctured torus and Lagrangian triangle groups in PU(2,1) ⋮ Classical Schottky groups of real type of genus two. II

Cites Work

• Unnamed Item
• All two generator Fuchsian groups
• A compactness theorem for Fuchsian groups of the second kind
• Doubly generated Fuchsian groups
• Two generator discrete free products
• On Poincaré's theorem for fundamental polygons
• Two generator Fuchsian groups of genus one
• Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung \(x^2+y^2+z^2=xyz\).
• Correction to Two generator Fuchsian groups of genus one

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