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Growth of fundamental groups and isoembolic volume and diameter


Author: Oguz C. Durumeric
Journal: Proc. Amer. Math. Soc. 130 (2002), 585-590
MSC (2000): Primary 53C20, 53C23
DOI: https://doi.org/10.1090/S0002-9939-01-06106-8
Published electronically: June 8, 2001
MathSciNet review: 1862141
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Abstract:

Some properties of fundamental groups of Riemannian manifolds $M$ will be studied without a lower bound assumption on Ricci curvature. The main method is to relate the local packing to global packing instead of using the Bishop-Gromov relative volume comparison. This method allows us to control the volume growth of the universal cover $\tilde{M}$ and yields bounds on the number of generators of $\pi_{1}(M)$ in terms of some isoembolic geometric invariants of $M$.


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Additional Information

Oguz C. Durumeric
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: odurumer@blue.weeg.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06106-8
Keywords: Isoembolic, fundamental group
Received by editor(s): July 31, 2000
Published electronically: June 8, 2001
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society

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