多重图的 clique 复合体、边膨胀和 tournaplexes
Clique complexes of multigraphs, edge inflations, and tournaplexes
AI总结：
本文研究了多重图的 clique 复合体的拓扑学，推广了 tournaplexes，并通过同调推论和 functorial 结果探讨了边膨胀复合体的同调计算。
摘要：
在本文中，我们介绍并研究了无环多重图的 clique 复合体的拓扑学。这些 clique 复合体推广了 tournaplexes，后者最近由 Govc、Levi 和 Smith 为研究大脑功能网络的拓扑学而引入。我们研究了一种通用的边膨胀 simplicial poset 构造，它推广了多重图的 clique 复合体。Björner、Wachs 和 Welker 的 poset 纤维定理被应用于获得边膨胀 simplicial poset 的同调楔分解。该结果的同调推论允许对边膨胀复合体的同调计算进行并行化，特别是对多重图的 clique 复合体和 tournaplexes。我们提供了某些结果的 functorial 版本，用于计算持久同调。最后，我们引入了 simplex 膨胀的一般概念，并为这一类空间证明了同伦楔分解。
英文摘要：
In this paper we introduce and study the topology of clique complexes of multigraphs without loops. These clique complexes generalize tournaplexes, which were recently introduced by Govc, Levi, and Smith for the topological study of brain functional networks. We study a general construction of edge-inflated simplicial posets, which generalize clique complexes of multigraphs. The poset fiber theorem of Björner, Wachs, and Welker is applied to obtain the homotopy wedge decomposition of an edge-inflated simplicial poset. The homological corollary of this result allows to parallelize the homology computations for edge inflated complexes, in particular, for clique complexes of multigraphs and tournaplexes. We provide functorial versions of some results to be used in computations of persistent homology. Finally, we introduce a general notion of simplex inflations and prove homotopy wedge decompositions for this class of spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
