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Geography of 4-manifolds with positive scalar curvature
Expositiones Mathematicae ( IF 0.7 ) Pub Date : 2021-06-02 , DOI: 10.1016/j.exmath.2021.05.003
Agnese Mantione , Rafael Torres

We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov’s observation that manifolds with positive scalar curvature tend to be inessential by focusing on the four-dimensional case. We also point out an strengthening of a result of Carr and its extension to the non-orientable realm.



中文翻译:

具有正标量曲率的 4 流形的地理

我们讨论了封闭定向 4 流形的地理问题,该流形允许正标量曲率的黎曼度量,并使用它来调查数学工作,以解决格罗莫夫的观察,即通过关注四维,具有正标量曲率的流形往往是无关紧要的案件。我们还指出了卡尔结果的加强及其对不可定向领域的扩展。

更新日期:2021-06-02
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