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A note on the fundamental groups of manifolds with almost nonnegative curvature

Author: Gabjin Yun
Journal: Proc. Amer. Math. Soc. 125 (1997), 1517-1522
MSC (1991): Primary 53C20; Secondary 57S20
MathSciNet review: 1371147
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Abstract: We show that given $n$ and $D, v >0$, there exists a positive number $ \epsilon = \epsilon (n,D,v)> 0$ such that if a closed $n$-manifold $M$ satisfies $Ric(M) \ge -\epsilon , diam(M) \le D$ and $vol(M) \ge v$, then $\pi _{1}(M)$ is almost abelian.

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Gabjin Yun
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
Address at time of publication: Department of Mathematics and GARC, Seoul National University, Seoul, Korea 151-742

Keywords: Almost non-negative curvature, almost nilpotent and abelian group
Received by editor(s): April 11, 1995
Received by editor(s) in revised form: November 29, 1995
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society