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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the existence of flat planes in spaces of nonpositive curvature
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by Martin R. Bridson PDF
Proc. Amer. Math. Soc. 123 (1995), 223-235 Request permission

Abstract:

Let X be a proper 1-connected geodesic metric space which is non-positively curved in the sense that it satisfies Gromov’s ${\text {CAT}}(0)$ condition globally. If X is cocompact, then either it is $\delta$-hyperbolic, for some $\delta > 0$, or else it contains an isometrically embedded copy of the Euclidean plane; these conditions are mutually exclusive. It follows that if the fundamental group of a compact non-positively curved polyhedron K is not word-hyperbolic, then the universal cover of K contains a flat plane.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 223-235
  • MSC: Primary 53C23; Secondary 20F32
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1273477-8
  • MathSciNet review: 1273477