The asphericity of random 2-dimensional complexes
The asphericity of random 2-dimensional complexes
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随机二维复合体的非球面性
DOI：
10.1002/rsa.20499
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发表时间：
2013
影响因子：
1
通讯作者：
Costa A
中科院分区：
文献类型：
--
作者：
Costa A
我们研究了线性- meshulam模型中的随机2维复合体，并证明了对于满足概率参数的随机2维复合体包含若干对不相交的四面体，使得从这些四面体中去除任意面得到的2维复合体是非球面的。并且证明了所得到的复形z满足Whitehead猜想，即任何子复形都是非球面的。这意味着y是同伦等价于一个楔形，而z是一个2维非球面单纯复合体。我们还证明了在假设bbb3和，络合物是真正的2维，特别是，它具有相当大的2维同调性；由此可见，在概率参数的指示范围内，随机2 -复数的基群的上同维数等于2。©2013 Wiley期刊公司随机结构。Alg。生态学报，46,261-273,2015
We study random 2‐dimensional complexes in the Linial–Meshulam model and prove that for the probability parameter satisfying a random 2‐complexYcontains several pairwise disjoint tetrahedra such that the 2‐complexZobtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complexZsatisfies the Whitehead conjecture, i.e. any subcomplex is aspherical. This implies thatYis homotopy equivalent to a wedge whereZis a 2‐dimensional aspherical simplicial complex. We also show that under the assumptions wherec> 3 and , the complexZis genuinely 2‐dimensional and in particular, it has sizable 2‐dimensional homology; it follows that in the indicated range of the probability parameterpthe cohomological dimension of the fundamental group of a random 2‐complex equals 2. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 261–273, 2015