Preprint

Inserted: 16 apr 2025
Last Updated: 16 apr 2025

Year: 2025

Abstract:

It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectures have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples $(M^{10}_k,g_k)$ with uniformly positive Ricci curvature $\mathrm{Ric}_{g_k}\ge 9$ whose fundamental groups cannot be uniformly virtually abelian.

Keywords: Ricci curvature, Fundamental group, Nilpotent

Download:

• Heisenberg160425.pdf