# Tagged mapping class groups: Auslander–Reiten translation

@article{Brstle2015TaggedMC,
title={Tagged mapping class groups: Auslander–Reiten translation},
author={Thomas Br{\"u}stle and Yu Qiu},
journal={Mathematische Zeitschrift},
year={2015},
volume={279},
pages={1103-1120}
}
• Published 30 November 2012
• Mathematics
• Mathematische Zeitschrift
We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $$\mathbf {S}$$S with marked points and non-empty boundary, which generalizes Brüstle–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 $$\mathrm{\mathcal {D} }(\Gamma _{\mathbf {S}})$$D(ΓS) associated to the surface and the corresponding Seidel–Thomas braid group of…

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