Ricci Curvature and Betti Numbers

Details Ricci Curvature and Betti Numbers Ricci Curvature and Betti Numbers

1994-11-07

arxiv.org/abs/dg-ga/9411003v1

Mathematics

Differential Geometry

18pages, Latex

Scientific paper

We derive a uniform bound for the total betti number of a closed manifold in terms of a Ricci curvature lower bound, a conjugate radius lower bound and a diameter upper bound. The result is based on an angle version of Toponogov comparison estimate for small triangles in a complete manifold with a Ricci curvature lower bound. We also give a uniform estimate on the generators of the fundamental group and prove a fibration theorem in this setting.

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