Detecting negative curvature in groups via local conditions

Shawcroft, Paul

doi:10.1090/S0002-9939-1994-1249891-2

Detecting negative curvature in groups via local conditions
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Proc. Amer. Math. Soc. 122 (1994), 1015-1023 Request permission

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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Detecting hyperbolicity

Identifying local structures in certain automatic groups