Gromoll--Meyer的作用与（奇异）时空的几何
Gromoll--Meyer's actions and the geometry of (exotic) spacetimes
AI总结：
本文提出一种计算方法，在经典和奇异球面上等变构造物理模型，首次在同胚但非微分同胚流形上实现具有相同物理性质的洛伦兹度量，并展望推广到更高维奇异球面。
摘要：
自从光滑流形上出现新的两两非微分同胚结构以来，人们一直质疑两个拓扑相同的流形是否能承认不同的几何。毫不奇怪，物理学家也想知道不同于某些经典已知模型的光滑结构假设是否会产生不同的物理意义。在本文中，我们开创了一种非常计算化的方式来在经典和奇异球面上构造物理模型，这些模型可以等变地构建，例如经典的Gromoll--Meyer奇异球面。作为初步应用，我们在同胚但非微分同胚的流形上构造了具有相同物理性质的洛伦兹度量，如测地完备性、正里奇曲率和相容的时间定向。这些构造可以拉回到更高维的模型，例如包围自旋流形的奇异十维球面，将在后续论文中探讨。
英文摘要：
Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a smooth structure assumption different from some classical known models could produce different physical meanings. In this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll--Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers.
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。
