The Cayley graph of a free group with two generators. This is a hyperbolic group whose Gromov boundary is a Cantor set. Hyperbolic groups and their boundaries are important topics in geometric group theory, as are Cayley graphs.The (6,4,2) triangular hyperbolic tiling. The triangle group corresponding to this tiling has a circle as its Gromov boundary.
In mathematics, the Gromov boundary of a δ-hyperbolic space (especially a hyperbolic group) is an abstract concept generalizing the boundary sphere of hyperbolic space. Conceptually, the Gromov boundary is the set of all points at infinity. For instance, the Gromov boundary of the real line is two points, corresponding to positive and negative infinity.
