论文标题
哪种簇态类别是猫（0）
Which cluster morphism categories are CAT(0)
论文作者
论文摘要
在[5]中引入了遗传代数的群集形态类别，以表明，有限表示类型的遗传代数的图片空间是相关图片组的$ K（π，1）$，从而允许计算[7]中有限类型的同源性的同性恋，以供[7]列出。 在本文中，我们表明，群集形态类别是$ cat（0）$ - 有限或温和类型的遗传代数类别，只有小管。结果，我们知道群集形态类别的分类空间是本地$ cat（0）$空间，因此，我们得到这个分类空间为$ k（π，1）$。
The cluster morphism category of an hereditary algebra was introduced in [5] to show that the picture space of an hereditary algebra of finite representation type is a $K(π,1)$ for the associated picture group, thereby allowing for the computation of the homology of picture groups of finite type as carried out in [7] for the case of $A_n$. In this paper we show that the cluster morphism category is a $CAT(0)$-category for hereditary algebras of finite or tame type with only small tubes. As a consequence, we get that the classifying space of the cluster morphism category is a locally $CAT(0)$ space and, as a consequence of that, we get that this classifying space is a $K(π,1)$.
