Topological regularity of Busemann spaces of nonpositive curvature
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917553846091776 |
|---|---|
| author | Fujioka, Tadashi Gu, Shijie |
| author_facet | Fujioka, Tadashi Gu, Shijie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological regularity of Busemann spaces of nonpositive curvature Fujioka, Tadashi Gu, Shijie Differential Geometry Geometric Topology Metric Geometry 53C23, 53C70, 57M50, 57N16, 57P05 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. |
| title | Topological regularity of Busemann spaces of nonpositive curvature |
| topic | Differential Geometry Geometric Topology Metric Geometry 53C23, 53C70, 57M50, 57N16, 57P05 |
| url | https://arxiv.org/abs/2504.14455 |