Tagged mapping class groups: Auslander-Reiten translation

Thomas Brüstle Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada Yu Qiu Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada; Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

Representation Theory mathscidoc:2206.30007

Mathematische Zeitschrift, 279, 1103-1120, 2015.1
We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface 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 D(Γ_S) associated to the surface and the corresponding Seidel–Thomas braid group of D(Γ_S) is empty, unless S is a polygon with at most one puncture (i.e. of type A or D).
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@inproceedings{thomas2015tagged,
  title={Tagged mapping class groups: Auslander-Reiten translation},
  author={Thomas Brüstle, and Yu Qiu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626164133709491463},
  booktitle={Mathematische Zeitschrift},
  volume={279},
  pages={1103-1120},
  year={2015},
}
Thomas Brüstle, and Yu Qiu. Tagged mapping class groups: Auslander-Reiten translation. 2015. Vol. 279. In Mathematische Zeitschrift. pp.1103-1120. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626164133709491463.
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