Growth of fundamental groups and isoembolic volume and diameter

Durumeric, Oguz

doi:10.1090/S0002-9939-01-06106-8

Growth of fundamental groups and isoembolic volume and diameter
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Proc. Amer. Math. Soc. 130 (2002), 585-590 Request permission

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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