Title: Topological regularity of Busemann spaces, Professor Tadashi Fujioka, Kyoto University

Abstract:

We discuss the topological regularity theorem for Busemann spaces of nonpositive curvature, while reviewing the corresponding results for Alexandrov spaces and CAT spaces. All of these are metric spaces with upper or lower curvature bounds in some synthetic senses, and we address the question of when such spaces are topological manifolds. This is joint work with Shijie Gu (Northeastern University, China). Preprint available at arXiv:2504.14455.

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