NONVANISHING OF ALGEBRAIC ENTROPY FOR GEOMETRICALLY FINITE GROUPS OF ISOMETRIES OF HADAMARD MANIFOLDS

DOI10.1142/S0218196705002682zbMath1107.20026arXivmath/0408160OpenAlexW2093385418MaRDI QIDQ3379470

Roger C. Alperin, Guennadi A. Noskov

Publication date: 6 April 2006

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408160

zbMATH Keywords

finitely generated groupsalgebraic entropyhyperbolic isometriesuniform exponential growthgeometrically finite groups of isometriesneutered spacespinched Hadamard manifolds

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Asymptotic properties of groups (20F69) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (3)

Uniform growth of groups acting on Cartan-Hadamard spaces. ⋮ Growth of relatively hyperbolic groups ⋮ Growth of discrete groups of isometries in negative curvature: a gap-property.

Cites Work

• Geometry of horospheres
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Uniform growth in hyperbolic groups
• Geometrical finiteness with variable negative curvature
• On exponential growth and uniformly exponential growth for groups.
• Distinguished subgroups and quotients of hyperbolic groups
• On problems related to growth, entropy, and spectrum in group theory
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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