Topological regularity of spaces with an upper curvature bound
Abstract
We prove that a locally compact space with an upper curvature bound is a topological manifold if and only if all of its spaces of directions are homotopy equivalent and not contractible. We discuss applications to homology manifolds, limits of Riemannian manifolds and deduce a sphere theorem.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2018
- DOI:
- 10.48550/arXiv.1809.06183
- arXiv:
- arXiv:1809.06183
- Bibcode:
- 2018arXiv180906183L
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Metric Geometry;
- 53C20;
- 53C23;
- 57P05