论文标题
多编码，边缘通货膨胀和循环的集团综合体
Clique complexes of multigraphs, edge inflations, and tournaplexes
论文作者
论文摘要
在本文中，我们介绍并研究了无循环的多编码集团复合物的拓扑结构。这些集团复合物概括了巡洋舰，这些曲线膜是Govc，Levi和Smith最近引入的，用于脑功能网络的拓扑研究。我们研究了边缘充气的简单posets的一般结构，该posets概括了多编码的集团复合物。 Björner，Wachs和Welker的POSET光纤定理用于获得边缘膨胀的简单poset的同型楔形分解。该结果的同源化学允许对边缘膨胀复合物的同源性计算，特别是对于多编码和巡回仪的集团复合物的同源计算。我们提供一些结果的功能版本，可用于持续同源性计算。最后，我们介绍了单纯膨胀的一般概念，并证明了这类空间的同型楔形分解。
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.
