Fundamental groups of open manifolds with nonnegative Ricci curvature and universal cover Euclidean volume growth

2025/07/31 by Chen, Lina
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.23690

Abstract

In this note, we will give an positive answer to Pan-Rong's conjecture that for an open manifold with nonnegative Ricci curvature, if its universal cover has Euclidean volume growth, then its fundamental group is finitely generated. Moreover the fundamental group is virtually abelian. The same result has been given by H.Huang-X.Huang for dimension 4. In fact, we will show the fundamental group finitely generated in a more general condition.

Citations

• Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open 4-Manifolds
• On the topology of manifolds with nonnegative Ricci curvature and linear volume growth
• Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost k-polar at infinity
• Six dimensional counterexample to the Milnor Conjecture
• Nonnegative Ricci curvature and escape rate gap
• Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups
• Ricci curvature and isometric actions with scaling nonvanishing property
• 3-manifolds with nonnegative Ricci curvature
• Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups

Related

• Nonnegative Ricci Curvature, Euclidean Volume Growth, and the Fundamental Groups of Open 4-Manifolds
• Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost k-polar at infinity
• Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups
• On the fundamental group of complete manifolds with almost Euclidean volume growth
• On the topology of manifolds with nonnegative Ricci curvature and linear volume growth