Locally $G$-homogeneous Busemann $G$-spaces
Geometric Topology
2011-05-10 v1 Differential Geometry
Metric Geometry
Abstract
We present short proofs of all known topological properties of general Busemann -spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally -homogeneous Busemann -spaces are homeomorphic and strongly topologically homogeneous. This is a key result in the context of the classical Busemann conjecture concerning the characterization of topological manifolds, which asserts that every -dimensional Busemann -space is a topological -manifold. We also prove that every Busemann -space which is uniformly locally -homogeneous on an orbal subset must be finite-dimensional.
Keywords
Cite
@article{arxiv.1105.1439,
title = {Locally $G$-homogeneous Busemann $G$-spaces},
author = {V. N. Berestovskiĭ and D. M. Halverson and D. Repovš},
journal= {arXiv preprint arXiv:1105.1439},
year = {2011}
}