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Relating Exponential Growth in a Manifold and Its Fundamental Group

Anthony Manning
Proceedings of the American Mathematical Society
Vol. 133, No. 4 (Apr., 2005), pp. 995-997
Stable URL: http://www.jstor.org/stable/4097657
Page Count: 3
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Relating Exponential Growth in a Manifold and Its Fundamental Group
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Abstract

We relate the growth rate of volume in the universal cover of a compact Riemannian manifold to the growth in the fundamental group in terms of word length in a given set of generators and the length of geodesics representing these generators.

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