Cotorsion pairs in the cluster category of a marked surface. (English) Zbl 1297.13028
The authors study the properties of cluster categories arising from unpunctured marked surfaces. A correspondence between curves on the surfaces and objects in the categories is given in [T. Brüstle and J. Zhang, Algebra Number Theory 5, No. 4, 529–566 (2011; Zbl 1250.16013)]. Under this correspondence, they show that the intersection number between curves corresponds to the dimension of \(\operatorname{Ext}^1\) between objects. Applications include the classification and geometric realization of cotorsion pairs (and their mutations) in these categories.
Reviewer: Yu Qiu (Trondheim)
MSC:
| 13F60 | Cluster algebras |
| 16G20 | Representations of quivers and partially ordered sets |
| 16G70 | Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |
Keywords:
marked surface; cluster category; cotorsion pair; \(t\)-structure; painting; mutation; rotationCitations:
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