论文标题
$ \ mathbf e $ -clusters a（iv）连续突变和几何模型的连续颤动
Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of $\mathbf E$-clusters
论文作者
论文摘要
如果这是$ a $ type type type Quivers中的最后一篇论文。在这一部分中，我们将$ a $ cluster结构的现有几何模型推广到（iii）中引入的新的$ \ mathbf e $ clusters。我们还引入了集群理论的同构和聚类理论的弱等效性。给出了两者的例子。我们使用群集理论的几何模型和同构来开始对连续类型$ a $ cluster结构进行分类。我们还引入了突变的连续概括。这包括突变的突变和（无限）突变序列。然后，我们将连续突变与早期的几何模型联系起来。最后，我们介绍了突变的空间，该突变概括了集群结构的交换图。
This if the final paper in the seriesContinuous Quivers of Type $A$. In this part, we generalize existing geometric models of type $A$ cluster structures to the new $\mathbf E$-clusters introduced in part (III). We also introduce an isomorphism of cluster theories and a weak equivalence of cluster theories. Examples of both are given. We use thes geometric models and isomorphisms of cluster theories to begin classifying continuous type $A$ cluster structures. We also introduce a continuous generalization of mutation. This encompasses mutation and (infinite) sequences of mutation. Then we link continuous mutation to our earlier geometric models. Finally, we introduce the space of mutations which generalizes the exchange graph of a cluster structure.
