Pinching estimates for negatively curved manifolds with nilpotent fundamental groups

Abstract

Let $M$ be a complete Riemannian metric of sectional curvature within $[-a^2,-1]$ whose fundamental group contains a $k$-step nilpotent subgroup of finite index. We prove that $a\ge k$ answering a question of M. Gromov. Furthermore, we show that for any $\epsilon >0$, the manifold $M$ admits a complete Riemannian metric of sectional curvature within $[-(k+\epsilon {)}^2,-1]$.

formula corrected, see page 7

References in corpus (1)

• Curvature bounds via Ricci smoothing

Cited by in corpus (1)

• On Higher Graph Manifolds