Morse-Novikov cohomology of almost nonnegatively curved manifolds

Abstract

Let $M^n$ be a closed manifold of almost nonnegative sectional curvature and nonzero first de Rham cohomology group. For any $[\theta ]\in H_{dR}^1(M^n),[\theta ]\ne 0$, we show that the Morse- Novikov cohomology group $H^p(M^n,\theta )$ vanishes for any $p$. A similar result holds for a closed manifold of almost nonnegative Ricci curvature under the additional assumption that its curvature operator is uniformly bounded from below.

References in corpus (2)

• Structure of fundamental groups of manifolds with Ricci curvature bounded below
• Characteristic varieties of nilpotent groups and applications