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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Detecting negative curvature in groups via local conditions


Author: Paul Shawcroft
Journal: Proc. Amer. Math. Soc. 122 (1994), 1015-1023
MSC: Primary 57M07; Secondary 20F10, 20F32, 53C23
MathSciNet review: 1249891
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Abstract: We characterize negative curvature of groups in terms of properties which can be checked locally in the Cayley graph. We prove the equivalence of these properties with the more familiar thin triangles property. We also present an algorithm which, when given a finite presentation of a group G, will recognize these properties in finite time if G is negatively curved.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1249891-2
PII: S 0002-9939(1994)1249891-2
Article copyright: © Copyright 1994 American Mathematical Society