BUSEMANN POINTS OF ARTIN GROUPS OF DIHEDRAL TYPE

Abstract

We study the horofunction boundary of an Artin group of dihedral type with its word metric coming from either the usual Artin generators or the dual generators. In both cases, we determine the horoboundary and say which points are Busemann points, that is, the limits of geodesic rays. In the case of the dual generators, it turns out that all boundary points are Busemann points, but this is not true for the Artin generators. We also characterize the geodesics with respect to the dual generators, which allows us to calculate the associated geodesic growth series.