发表机构
London Institute for Mathematical Sciences, Royal Institution; Merton College, University of Oxford; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS); Research Institute of Intelligent Complex Systems, Fudan University; Yau Mathematical Sciences Center, Tsinghua University（伦敦数学科学研究所，皇家学会; 牛津大学默顿学院; 上海数学与交叉学科研究院（SIMIS）; 复旦大学复杂系统智能研究院; 清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在所有28个有向微分同胚类的光滑同伦七球面上构造了具有严格正截面曲率的黎曼度量，通过两个七维圆盘的正曲率度量粘合实现。
AI 中文摘要
我们在每个光滑同伦七球面上构造了一个具有严格正截面曲率的平滑黎曼度量。对于每个光滑结构，我们在两个七维圆盘上构造正曲率度量，其诱导的边界度量在规定的粘合映射下一致。在此识别下，粘合定理随后在闭流形上产生所需的平滑度量。该构造适用于所有28个有向微分同胚类。
英文摘要
We construct a smooth Riemannian metric with strictly positive sectional curvature on every smooth homotopy seven-sphere. For each smooth structure, we construct positively curved metrics on two seven-dimensional disks whose induced boundary metrics agree under the prescribed attaching map. Under this identification, a gluing theorem then yields the required smooth metric on the closed manifold. The construction applies to all 28 oriented diffeomorphism classes.
Comments32 pages
