On the cluster category of a marked surface without punctures
On the cluster category of a marked surface without punctures
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DOI：
10.2140/ant.2011.5.529
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发表时间：
2010-05
影响因子：
1.3
通讯作者：
T. Brustle;Jie Zhang
中科院分区：
文献类型：
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作者：
T. Brustle;Jie Zhang
本文研究了标记曲面（S，M）的簇范畴C（S，M）.我们将C（S，M）中的对象明确描述为（S，M）中曲线的同伦类和与（S，M）中闭曲线相关的单参数族的直接和。此外，我们用几何术语描述了范畴C（S，M）的Auslander-Reiten结构，并证明了C（S，M）中没有自扩张的对象对应于（S，M）中没有自相交的曲线.因此，我们建立了每一个刚性的不可分解的对象是从一个初始的三角形。
We study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M). Moreover, we describe the Auslander-Reiten structure of the category C(S,M) in geometric terms and show that the objects without self-extensions in C(S,M) correspond to curves in (S,M) without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation.