Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility networks. We empirically demonstrate that these human mobility network localities are rigorous geometric entities that map directly to geographic localities, revealing that human mobility networks lie on manifolds of dimension <=5. This representation provides a compact theoretical foundation for spatial embedding and enables efficient applications to facility location and propagation modeling. Our approach reconciles local heterogeneity with universal representation, offering a new pathway toward a more comprehensive urban science.

翻译：城市科学长期以来主要依赖普适性模型，这使得城市异质性与地域特定性本质在研究中近乎隐形。本文提出一种拓扑框架，用于定义和检测人类移动网络中的局部性结构。我们通过实证研究表明，这些人类移动网络局部性是严格的几何实体，能够直接映射到地理局部区域，并揭示人类移动网络存在于维度≤5的流形上。该表征为空间嵌入提供了紧凑的理论基础，并能够高效应用于设施选址与传播建模。我们的方法将局部异质性与普适性表征相统一，为构建更全面的城市科学开辟了新路径。