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


Author: P. D. Andreev
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 26 (2014), nomer 2.
Journal: St. Petersburg Math. J. 26 (2015), 193-206
MSC (2010): Primary 53C70
DOI: https://doi.org/10.1090/S1061-0022-2015-01336-8
Published electronically: February 3, 2015
MathSciNet review: 3242034
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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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Additional Information

P. D. Andreev
Affiliation: Northern (Arctic) Lomonosov Federal University, 17, nab. Severnoĭ Dviny, Arkhangelsk 163002, Russia
Email: pdandreev@mail.ru

DOI: https://doi.org/10.1090/S1061-0022-2015-01336-8
Keywords: $G$-spaces, nonpositive curvature, Busemann conjecture
Received by editor(s): April 12, 2013
Published electronically: February 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society