A geometric description of the $m$-cluster categories of type $D_n$



We show that the $m$-cluster category of type $D_n$ 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 $m$th power of a translation quiver to realise the $m$-cluster category in terms of the cluster category.

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