A Geometric Description of the m-Cluster Categories of Type D_n

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 generalises a result of Schiffler for m=1. We use the notion of the mth power of translation quiver to realise the m-cluster category in terms of the cluster category.