Abstract
We study the cluster category of a marked surface without punctures. We explicitly describe the objects in as direct sums of homotopy classes of curves in and one-parameter families related to noncontractible closed curves in . Moreover, we describe the Auslander–Reiten structure of the category in geometric terms and show that the objects without self-extensions in correspond to curves in without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation.
Citation
Thomas Brüstle. Jie Zhang. "On the cluster category of a marked surface without punctures." Algebra Number Theory 5 (4) 529 - 566, 2011. https://doi.org/10.2140/ant.2011.5.529
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