Tagged mapping class groups: Auslander-Reiten translation

We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface with marked points and non-empty boundary, which generalizes Brustle-Zhang's result for the puncture free case. As an application, we show that the intersection of the shifts in the 3-Calabi-Yau derived category associated to the surface and the corresponding Seidel-Thomas braid group of is empty, unless is a polygon with at most one puncture (i.e. of type A or D).