Accepted Paper

Inserted: 16 apr 2025
Last Updated: 28 may 2026

Journal: Comm. Pure Appl. Math.
Year: 2025

Abstract:

It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has a uniformly almost nilpotent fundamental group. Leftover questions and conjectures ask whether, in this context, the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples $(M^{9}_k, g_k)$ with uniformly positive Ricci curvature ${\rm Ric}_{g_k}\geq 8$ whose fundamental groups cannot be uniformly virtually abelian.

Keywords: Ricci curvature, Fundamental group, Nilpotent

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