Nonnegative Ricci curvature, metric cones, and virtual abelianness
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913357241516032 |
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| author | Pan, Jiayin |
| author_facet | Pan, Jiayin |
| contents | Let $M$ be an open $n$-manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $1/2$ 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 $π_1(M)$ 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 $C(n,L)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_07852 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonnegative Ricci curvature, metric cones, and virtual abelianness Pan, Jiayin Differential Geometry Let $M$ be an open $n$-manifold with nonnegative Ricci curvature. We prove that if its escape rate is not $1/2$ 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 $π_1(M)$ 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 $C(n,L)$. |
| title | Nonnegative Ricci curvature, metric cones, and virtual abelianness |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2201.07852 |