Proof of the Busemann conjecture for 𝐺-spaces of nonpositive curvature

Andreev, P.

doi:10.1090/S1061-0022-2015-01336-8

Proof of the Busemann conjecture for $G$-spaces of nonpositive curvature
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by P. D. Andreev
Translated by: S. Kislyakov

St. Petersburg Math. J. 26 (2015), 193-206

DOI: https://doi.org/10.1090/S1061-0022-2015-01336-8

Published electronically: February 3, 2015

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Abstract:

It is proved that every simply connected Busemann $G$-space of nonpositive curvature is homeomorphic to $\mathbb R^n$ for some positive integer $n$. As a consequence, the well-known conjecture that every Busemann $G$-space is a topological manifold becomes confirmed for the $G$-spaces of nonpositive curvature.

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