Detecting Negative Curvature in Groups Via Local Conditions

Paul Shawcroft
1994 Proceedings of the American Mathematical Society  
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.
doi:10.2307/2161168 fatcat:nvs4yewxsvbjznnzvjaz2x4x6u