论文标题
匹配，摩尔斯和广义摩尔斯综合体中的明星簇
Star clusters in the Matching, Morse, and Generalized Morse complex
论文作者
论文摘要
在本文中，我们通过利用恒星簇倒塌和簇引理来确定多个复合物家族的Morse复合物的同型类型和匹配的复合物。我们计算恒星图的扩展概念的摩尔斯复合物的同喻类型，以及荷兰风车图的匹配复合物的同型类型。此外，我们还提供了路径摩尔斯摩尔斯复合物，路径匹配络合物的同质型的同质类型的替代计算以及循环匹配复合物的同型类型。然后，我们使用相同的计算同质类型的方法来研究匹配复合物的同拷贝类型与广义摩尔斯复合物之间的关系。
In this paper, we determine the homotopy type of the Morse complex and matching complex of multiple families of complexes by utilizing star cluster collapses and the Cluster Lemma. We compute the homotopy type of the Morse complex of an extended notion of a star graph, as well as the homotopy type of the matching complex of a Dutch windmill graph. Additionally, we provide alternate computations of the homotopy type of the Morse complex of paths, the homotopy type of the matching complex of paths, and the homotopy type of the matching complex of cycles. We then use this same method of computing homotopy types to investigate the relationship between the homotopy type of the matching complex and the generalized Morse complex.
