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arXiv · 1212.0007

Tagged mapping class groups: Auslander-Reiten translation

Thomas Brüstle·Yu Qiu
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Abstract

We give a geometric realization, the tagged rotation, of the AR-translation on the generalized cluster category associated to a surface $\mathbf{S}$ 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 $\mathcal{D}(Γ_{\mathbf{S}})$ associated to the surface and the corresponding Seidel-Thomas braid group of $\mathcal{D}(Γ_{\mathbf{S}})$ is empty, unless $\mathbf{S}$ is a polygon with at most one puncture (i.e. of type A or D).

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BibTeXRIS

Thomas Brüstle, Yu Qiu. 2014-11-05. Tagged mapping class groups: Auslander-Reiten translation. https://doi.org/10.1007/s00209-015-1405-z

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