Almost splitting maps, transformation theorems and smooth fibration theorems

Huang, Hongzhi; Huang, Xian-Tao

doi:10.1016/j.aim.2024.109914

Advances in Mathematics

2024

DOI: 10.1016/j.aim.2024.109914

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Almost splitting maps, transformation theorems and smooth fibration theorems

Hongzhi Huang,

Xian-Tao Huang

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2024

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Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost 𝑘-polar at infinity

Huang

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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In this article, we prove that the fundamental group π 1 ⁢ ( M ) \pi_{1}(M) of a complete open manifold 𝑀 with nonnegative Ricci curvature is finitely generated, under the condition that the Riemannian universal cover M ̃ \tilde{M} satisfies an “almost 𝑘-polar at infinity” condition. Additionally, such π 1 ⁢ ( M ) \pi_{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 M ̃ \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.

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Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost 𝑘-polar at infinity

Huang

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

show abstract

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Almost splitting maps, transformation theorems and smooth fibration theorems

Cited by 1 publication

References 44 publications

Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost 𝑘-polar at infinity

Finite generation of fundamental groups for manifolds with nonnegative Ricci curvature whose universal cover is almost 𝑘-polar at infinity

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