高度连通的7流形和非负截面曲率

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2020-01-01 DOI:10.4007/annals.2020.191.3.3

S. Goette, M. Kerin, K. Shankar

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引用次数: 26

摘要

摘要:构造了具有非负截面曲率的SO(3)不变度量的六参数高连通7流形族，并计算了它们的Eells-Kuiper不变量。特别地，可以得出，所有在7维的奇异球都有一个非负曲率的SO(3)不变度规。

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Highly connected 7-manifolds and non-negative sectional curvature

Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO (3) -invariant metric of non-negative curvature.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.