A Geometric Description of the m-cluster Categories of Type Dn

We show that the m-cluster category of type Dn is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm−m+1-gon. This generalizes a result of Schiffler for m=1. We use the notion of the mth power of a translation quiver to realize the m-cluster category in terms of the cluster category.