An Approach to the Study of Finitely Presented Groups Based on the Notion of Discrete Curvature

Abstract

A sufficient condition for the hyperbolicity of a group presented in terms of generators and defining relations is considered. The condition is formulated in terms of the negativity of a discrete analog of curvature for the Lyndon–van Kampen diagrams over a presentation of a group and is a generalization of the small cancellation condition.