Topological regularity of spaces with an upper curvature bound
Differential Geometry
2018-09-18 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.1809.06183,
title = {Topological regularity of spaces with an upper curvature bound},
author = {Alexander Lytchak and Koichi Nagano},
journal= {arXiv preprint arXiv:1809.06183},
year = {2018}
}