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arXiv · 1311.0010

Cluster categories for marked surfaces: punctured case

Yu Qiu·Yu Zhou
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Abstract

We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of $\operatorname{Ext}^1$ as intersection numbers of tagged curves and Auslander-Reiten translation as tagged rotation. An important consequence is that the cluster(-tilting) exchange graphs of such cluster categories are connected.

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Yu Qiu, Yu Zhou. 2013-10-31. Cluster categories for marked surfaces: punctured case. https://doi.org/10.1112/s0010437x17007229

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