Orbifolds with Lower Ricci Curvatur E Bounds
نویسنده
چکیده
We show that the first betti number b1 (0) = d im H 1(0, !R) of a compact Riemannian orbifold 0 with Ricci curvature Ric(O ) ~ -(n 1)k and d iameter diam(O) :5 D is bounded above by a constant r (n, kD2 ) ~ 0 , depending only on dimension , curvature and diameter. In the case when t he orbi fold has nonnegative Ricci curvature, we show that the b1 (0) is bounded above by the dimension dim 0 , and that if, in addition, b1 (0 ) =dim 0 , then 0 is a Rat torus T" .
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