NONVANISHING OF ALGEBRAIC ENTROPY FOR GEOMETRICALLY FINITE GROUPS OF ISOMETRIES OF HADAMARD MANIFOLDS-Reference-Cited by-同舟云学术

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

Published:2005-10 Issue:05n06 Volume:15 Page:799-813
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

ALPERIN ROGER C.¹,NOSKOV GENNADY A.²³

Affiliation:

1. Dept. of Mathematics, San Jose State University, San Jose, CA 95192, USA

2. Institute of Mathematics, Russian Academy of Sciences, Pevtsova 13, Omsk, 644099, Russia

3. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

Abstract

We prove that any nonelementary geometrically finite group of isometries of a pinched Hadamard manifold has nonzero algebraic entropy in the sense of M. Gromov. In other words it has uniform exponential growth.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196705002682

Reference18 articles.

1. J. M. Alonso, Group Theory from a Geometrical Viewpoint (Trieste, 1990), ed. H. Short (World Scientific, River Edge, NJ, 1991) pp. 3–63.

2. Uniform growth, actions on trees and 𝐺𝐿₂

3. Manifolds of Nonpositive Curvature

4. Geometrical finiteness with variable negative curvature

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Uniform growth of groups acting on Cartan–Hadamard spaces;Journal of the European Mathematical Society;2011

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