Topological regularity of Busemann spaces of nonpositive curvature
Differential Geometry
2025-05-09 v2 Geometric Topology
Metric Geometry
Abstract
We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We give a characterization of locally BNPC topological manifolds in terms of their links and show that the singular set of a locally BNPC homology manifold is discrete. We also prove that any (globally) BNPC topological 4-manifold is homeomorphic to Euclidean space. Applications include a topological stability theorem for locally BNPC G-spaces. Our arguments also apply to spaces admitting convex geodesic bicombings.
Cite
@article{arxiv.2504.14455,
title = {Topological regularity of Busemann spaces of nonpositive curvature},
author = {Tadashi Fujioka and Shijie Gu},
journal= {arXiv preprint arXiv:2504.14455},
year = {2025}
}
Comments
added Remark 3.2, revised Problem 8.6, added and removed references, and made other minor changes, mainly in Section 8