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Ricci Curvature and Betti Numbers

Guofang Wei
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Abstract

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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BibTeXRIS

Guofang Wei. 1994-11-07. Ricci Curvature and Betti Numbers. https://arxiv.org/abs/dg-ga/9411003

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