Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
Differential Geometry
2019-08-13 v2 Geometric Topology
Abstract
We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case we prove a strengthened Price inequality. We employ these inequalities to study the asymptotic behavior of the Betti numbers of coverings of Riemannian manifolds without conjugate points. Finally, we give a vanishing result for -Betti numbers of closed manifolds without conjugate points.
Keywords
Cite
@article{arxiv.1704.06354,
title = {Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points},
author = {Luca F. Di Cerbo and Mark Stern},
journal= {arXiv preprint arXiv:1704.06354},
year = {2019}
}
Comments
Some changes and typos corrected following referees' reports. To appear in Comm. Anal. Geom., 31 pages