Fundamental Groups of Manifolds with Positive Sectional Curvature and Torus Symmetry
Fundamental Groups of Manifolds with Positive Sectional Curvature and Torus Symmetry
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DOI：
10.1007/s12220-017-9787-2
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发表时间：
2017-03
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影响因子：
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通讯作者：
Lee Kennard
中科院分区：
文献类型：
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作者：
Lee Kennard
在1965年，陈省身提出了一个问题，在何种程度上承认积极的截面曲率流形基本群体看起来像球面空间形式组。最初的问题在1998年被Shankar否定地回答，但在对称性的存在下有许多积极的结果。这些分类根据其结论的强度而分为不同的类别。我们给出了一个概述，这些结果的情况下，环面对称性，并证明在这些类别中的每一个新的结果。
In 1965, Chern posed a question concerning the extent to which fundamental groups of manifolds admitting positive sectional curvature look like spherical space form groups. The original question was answered in the negative by Shankar in 1998, but there are a number of positive results in the presence of symmetry. These classifications fall into categories according to the strength of their conclusions. We give an overview of these results in the case of torus symmetry and prove new results in each of these categories.