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The aim of this note is to answer several open problems arising from thegeometric description of the $m$-cluster categories of type $A_n$ and theirrealization in terms of the $m$-th power of a translation quiver. Inparticular, we give a geometric interpretation of the triangulated structure of$m$-cluster categories. Furthermore, we characterize all the connectedcomponents arising from a cluster category when taking the $m$-th power of itsAuslander-Reiten quiver.

A geometric interpretation of the triangulated structure of m-cluster categories