Cluster categories for marked surfaces: punctured case

Qiu Yu Chinese University of Hong Kong Yu Zhou Norwegian University of Science and Technology

Category Theory Representation Theory Rings and Algebras mathscidoc:1906.04001

Compositio Math, 153, 1779-1819, 2017
We study cluster categories arising from marked surfaces (with punctures and nonempty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting dimensions of Ext1 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.
cluster categories, intersection numbers, cluster exchange graphs, skewed-gentle algebras
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@inproceedings{qiu2017cluster,
  title={Cluster categories for marked surfaces: punctured case},
  author={Qiu Yu, and Yu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625212220578921360},
  booktitle={Compositio Math},
  volume={153},
  pages={1779-1819},
  year={2017},
}
Qiu Yu, and Yu Zhou. Cluster categories for marked surfaces: punctured case. 2017. Vol. 153. In Compositio Math. pp.1779-1819. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190625212220578921360.
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