1994/11/07 by Wei, Guofang
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.dg-ga/9411003
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.