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Orbifolds with lower Ricci curvature bounds

Author: Joseph E. Borzellino
Journal: Proc. Amer. Math. Soc. 125 (1997), 3011-3018
MSC (1991): Primary 53C20
MathSciNet review: 1415575
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Abstract: We show that the first betti number $b_1(O)=\dim \,H_1(O,{\mathbb R})$ of a compact Riemannian orbifold $O$ with Ricci curvature $\operatorname {Ric}(O)\ge -(n-1)k$ and diameter $\operatorname {diam}(O)\le D$ is bounded above by a constant $c(n,kD^2)\ge 0$, depending only on dimension, curvature and diameter. In the case when the orbifold has nonnegative Ricci curvature, we show that the $b_1(O)$ is bounded above by the dimension $\dim \,O$, and that if, in addition, $b_1(O)=\dim \,O$, then $O$ is a flat torus $T^n$.

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Additional Information

Joseph E. Borzellino

Received by editor(s): May 15, 1996
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society