Ricci curvature and betti numbers
Copyright policy )Ricci curvature and betti numbers
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.
18pages, Latex
- University of California, Santa Barbara United States
Mathematics - Differential Geometry, Ricci curvature, Toponogov comparison estimate, Differential Geometry (math.DG), conjugate radius, FOS: Mathematics, diameter, fibration theorem, Global Riemannian geometry, including pinching, total Betti number, fundamental group
Mathematics - Differential Geometry, Ricci curvature, Toponogov comparison estimate, Differential Geometry (math.DG), conjugate radius, FOS: Mathematics, diameter, fibration theorem, Global Riemannian geometry, including pinching, total Betti number, fundamental group
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!