Hyperbolic group

Summary

A hyperbolic group is a finitely generated group whose Cayley graph looks like a tree at large scale: its geodesic triangles are uniformly thin. The notion was introduced by Gromov. It covers free groups, fundamental groups of closed hyperbolic manifolds, and, in a precise sense, most finitely presented groups. Hyperbolic groups are finitely presented, have a solvable word problem and conjugacy problem, and have a linear Dehn function.