Large random simplicial complexes, II; the fundamental group
Large random simplicial complexes, II; the fundamental group
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大型随机单纯复形，II；
DOI：
10.1142/s1793525317500170
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发表时间：
2016
影响因子：
0.8
通讯作者：
Costa A
中科院分区：
文献类型：
--
作者：
Costa A
我们研究多参数模型中的随机单纯复形，主要关注基本群的属性。我们描述了这些组的非平凡性和双曲性（格罗莫夫意义上的）的阈值。此外，我们在多参数空间中找到了这些群具有 2 扭转的域。我们还证明这些群永远不会有奇素数挠率，并且它们的几何维数和上同调维数要么是 0、1、2 要么。本文提出的另一个结果表明，随机复形的非球面二维子复形满足怀特海猜想，即它们的所有子复形也是非球面的，概率趋于1。
We study random simplicial complexes in the multi-parameter model focusing mainly on the properties of the fundamental groups. We describe thresholds for nontrivially and hyperbolicity (in the sense of Gromov) for these groups. Besides, we find domains in the multi-parameter space where these groups have 2-torsion. We also prove that these groups never have odd-prime torsion and their geometric and cohomological dimensions are either 0, 1, 2 or. Another result presented in this paper states that aspherical 2-dimensional subcomplexes of random complexes satisfy the Whitehead Conjecture, i.e. all their subcomplexes are also aspherical, with probability tending to one.