Price inequalities and Betti number growth on manifolds without conjugate points

摘要

We derive Price inequalities for harmonic forms on manifolds with-out 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.