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- W2894464839 abstract "We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $widetilde{M}$ at infinity is a metric cone, whose cross-section is sufficiently Gromov-Hausdorff close to a prior fixed metric space, then $pi_1(M)$ is finitely generated and contains a normal abelian subgroup of finite index; if in addition $widetilde{M}$ has Euclidean volume growth of constant at least $L$, then we can bound the index of that abelian subgroup in terms of $n$ and $L$. In particular, our result implies that if $widetilde{M}$ has Euclidean volume growth of constant at least $1-epsilon(n)$, then $pi_1(M)$ is finitely generated and $C(n)$-abelian." @default.
- W2894464839 created "2018-10-05" @default.
- W2894464839 creator A5055714225 @default.
- W2894464839 date "2018-09-26" @default.
- W2894464839 modified "2023-09-27" @default.
- W2894464839 title "Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups" @default.
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