Ricci Curvature and Betti Numbers
dg-ga
2008-02-03 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.dg-ga/9411003,
title = {Ricci Curvature and Betti Numbers},
author = {Guofang Wei},
journal= {arXiv preprint arXiv:dg-ga/9411003},
year = {2008}
}
Comments
18pages, Latex