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

Author(s): 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.

References:

[1]: M. T. Anderson, Short geodesics and gravitational instantons, J. Diff. Geometry 31 (1990), 265-275. MR 91b:53040
[2]: -, On the topology of complete manifolds of nonnegative Ricci curvature, Topology 29 (1990), 41-55. MR 91b:53041
[3]: J. Cheeger and T. Colding, preprint.
[4]: J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Diff. Geometry 6 (1971), 119-128. MR 46:2597
[5]: T. Colding, Ricci curvature and volume convergence, preprint.
[6]: K. Fukaya, Theory of convergence for Riemannian orbifolds, Iapan J. Math. 12 (1986), 121-160. MR 89d:53083
[7]: K. Fukaya and T. Yamaguchi, The fundamental groups of almost nonnegatively curved manifolds, Ann. Math. 136 (1992), 253-333. MR 93h:53041
[8]: M. Gromov, (rédige par J. Lafontaine et P. Pansu), Structure métrique pour les variété riemanniennes, Cedic/Fernand Nathan, Paris, 1982. MR 85e:53051
[9]: -, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. No. 53 (1981), 53-73. MR 83b:53041
[10]: J. Milnor, A note on curvature and fundamental group, J. Diff Geometry 2 (1968), 1-7. MR 38:636
[11]: M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, Berlin, 1972. MR 58:22394a
[12]: G. Wei, On the fundamental groups of manifolds with almost nonnegative Ricci curvature, Proc. Amer. Math. Soc 110 (1990), 197-199. MR 90m:53058
[13]: J. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geometry 2 (1968), 421-446. MR 40:1939
[14]: T. Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. 133 (1991), 317-357. MR 92b:53067
[15]: -, Manifolds of almost nonnegative curvature, MPI, 1993.

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Additional Information:

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
Email: gabjin@math.snu.ac.kr

DOI: 10.1090/S0002-9939-97-03756-8
PII: S 0002-9939(97)03756-8
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
Copyright of article: Copyright 1997, American Mathematical Society

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