标题： Auslander-Reiten理论对于单连通微分分次代数 显示英文标题

标题： Auslander-Reiten theory for simply connected differential graded algebras

摘要： 彼得·约根森引入了单连通的庞加莱对偶空间的Auslander-Reiten图。他证明了其组成部分的形式为ZA_∞，并且d维球面的Auslander-Reiten图由d-1个这样的组成部分构成。在本论文中，我们证明这是唯一出现有限多个组成部分的情况。更准确地说，我们构造了模块族，其中对于每个族，每个模块位于不同的组成部分中。根据出现的微分分次代数的上同调维度，这要么是一个离散族，要么是所有n的n参数族。 显示英文摘要

摘要： Peter Jorgensen introduced the Auslander-Reiten quiver of a simply connected Poincare duality space. He showed that its components are of the form ZA_infty and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d-1 such components. In this thesis we show that this is the only case where finitely many components appear. More precisely, we construct families of modules, where for each family, each module lies in a different component. Depending on the cohomology dimensions of the differential graded algebras which appear, this is either a discrete family or an n-parameter family for all n.