Locally $G$-homogeneous Busemann $G$-spaces

V. N. Berestovskiĭ; D. M. Halverson; D. Repovš

doi:10.1016/j.difgeo.2011.03.001

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arXiv · 1105.1439

Locally $G$-homogeneous Busemann $G$-spaces

V. N. Berestovskiĭ·D. M. Halverson·D. Repovš

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Abstract

We present short proofs of all known topological properties of general Busemann $G$-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally $G$-homogeneous Busemann $G$-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 $n$-dimensional Busemann $G$-space is a topological $n$-manifold. We also prove that every Busemann $G$-space which is uniformly locally $G$-homogeneous on an orbal subset must be finite-dimensional.

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BibTeX RIS

V. N. Berestovskiĭ, D. M. Halverson, D. Repovš. 2011-05-07. Locally $G$-homogeneous Busemann $G$-spaces. https://doi.org/10.1016/j.difgeo.2011.03.001

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