Communications in Analysis and Geometry
Volume 30 (2022)
Price inequalities and Betti number growth on manifolds without conjugate points
Pages: 297 – 334
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 $L^2$-Betti numbers of closed manifolds without conjugate points.
The first-named author was partially supported by a grant associated to the S. S. Chern position at ICTP.
The second-named author was partially supported by Simons Foundation Grant 3553857.
Received 16 May 2018
Accepted 9 August 2019
Published 29 November 2022