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arXiv · 2504.14455

Topological regularity of Busemann spaces of nonpositive curvature

Tadashi Fujioka·Shijie Gu
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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.

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Tadashi Fujioka, Shijie Gu. 2025-04-20. Topological regularity of Busemann spaces of nonpositive curvature. https://arxiv.org/abs/2504.14455

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