“Holiverse”：$\R^3$中2-球的整体外翻
The `Holiverse': holistic eversion of the 2-sphere in $\R^3$
摘要：
我们给出了一个简短的，简单的和概念性的证明，基于自旋结构，球的外翻：一个嵌入的2-球面$R^3$可以翻转内到外的正则同伦。这种外翻的成分是无缝连接的。我们也给出了证明的数学起源：Hopf纤维化，和实射影三维空间的拓扑结构。
英文摘要：
We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in $R^3$ can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological structure of real-projective 3-space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
