Nonnegative Ricci curvature, metric cones and virtual abelianness

Pan, Jiayin¹

¹ Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada, Mathematics Department, University of California, Santa Cruz, Santa Cruz, CA, United States

Geometry & topology, Tome 28 (2024) no. 3, pp. 1409-1436.

Résumé

Let $M$ be an open $n$–manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $\frac{1}{2}$ and its Riemannian universal cover is conic at infinity (that is, every asymptotic cone $(Y,y)$ of the universal cover is a metric cone with vertex $y$), then ${\pi }_1(M)$ contains an abelian subgroup of finite index. If in addition the universal cover has Euclidean volume growth of constant at least $L$, we can further bound the index by a constant $C(n,L)$.

Détail

DOI : 10.2140/gt.2024.28.1409

Keywords: Ricci curvature, fundamental groups

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