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Summary: Nonvanishing of algebraic entropy for
geometrically finite groups of isometries of
Hadamard manifolds
Roger C. Alperin
San Jose State University, San Jose, CA, USA
Gennady A. Noskov
Bielefeld University, GERMANY and
Institute of Mathematics, Omsk, RUSSIA
February 14, 2003
Abstract
We prove that any nonelementary geometrically finite group of
isometries of a pinched Hadamard manifold has nonzero algebraic en-
tropy in the sense of M. Gromov. In other words it has a uniform
exponential growth,
1 Introduction
Given a group generated by a finite set S we denote by BS(r) the the ball
of radius k in the Cayley graph of relative to S. The exponential growth
rate or (, S) = limk
k
|BS(k)| is well defined (by submultiplicativity).
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