Large random simplicial complexes, III the critical dimension
Large random simplicial complexes, III the critical dimension
复制标题
大型随机单纯复形，III 临界维数
DOI：
10.1142/s0218216517400107
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发表时间：
2017
影响因子：
0.5
通讯作者：
Costa A
中科院分区：
文献类型：
--
作者：
Costa A
在这篇文章中，我们研究了一般多参数模型中随机单纯复形的临界维度的概念[随机单纯复形，预印本(2014年)，arxiv：1412.5805；大型随机单纯复形，I，预印本(2015年)，arxiv：1503.06285；大型随机单纯复形，II，预印本(2015年)，arxiv：1509.04837]。该模型包括作为特例的Linial-Meshulam-Wallach模型[随机2-复合体的同调连通性，Combinatorica26(2006)475-487；随机复合体的同调连通性，随机结构。邮编：34(2009)408-417。]以及随机图的团复合体。利用随机单纯形的Betti数、基本群、极小圈的大小和单纯形度等几何和拓扑性质刻画了临界维的概念。我们在课文中提到了几个有趣的开放问题。
In this paper, we study the notion of critical dimension of random simplicial complexes in the general multi-parameter model described in [Random simplicial complexes, preprint (2014), arXiv:1412.5805; Large random simplicial complexes, I, preprint (2015), arXiv:1503.06285; Large random simplical complexes, II, preprint (2015), arXiv:1509.04837]. This model includes as special cases the Linial–Meshulam–Wallach model [Homological connectivity of random 2-complexes,Combinatorica26(2006) 475–487; Homological connectivity of random-complexes,Random Struct. Alogrithms34(2009) 408–417.] as well as the clique complexes of random graphs. We characterize the concept of critical dimension in terms of various geometric and topological properties of random simplicial complexes such as their Betti numbers, the fundamental group, the size of minimal cycles and the degrees of simplexes. We mention in the text a few interesting open questions.