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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2312.00182 |
| Etiquetas: |
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- In this article, we prove that the fundamental group $π_1(M)$ of a complete open manifold $M$ with nonnegative Ricci curvature is finitely generated, under the condition that the Riemannian universal cover $\tilde M$ satisfies an "almost $k$-polar at infinity" condition. Additionally, such $π_1(M)$ is virtually abelian. Furthermore, we demonstrate that the base point of any tangent cone at infinity of such a manifold is nearly a pole. In the case where $\tilde M$ exhibits almost maximal Euclidean volume growth, we prove that $M$ deformation retracts to a closed submanifold $F$ which is diffeomorphic to a flat manifold, provided $M$ is not simply connected.