Criteria for asphericity of polyhedral products: corrigenda to “right-angularity, flag complexes, asphericity”
Criteria for asphericity of polyhedral products: corrigenda to “right-angularity, flag complexes, asphericity”
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多面体产品的非球面度标准：“直角度、旗形复合体、非球面度”的更正
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
P. Kropholler
中科院分区：
文献类型：
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作者：
Michael W. Davis;P. Kropholler
给定一个顶点集为I的单纯复形L L和一个基点在B（i）中的空间对的族A ={（A（i），B（i））}i∈I，存在A关于L的“多面体积”AL的定义.有时这被称为“广义矩角复合体”。本说明涉及对第一作者早期工作的两个改进。首先，当$$L$$L是无限大时，多面体积的定义需要澄清。第二，前面的文章省略了多面体积是非球面的充分必要条件中的一些微妙的部分。本文给出了这些充分必要条件的正确形式。
Given a simplicial complex $$L$$L with vertex set $$I$$I and a family $${mathbf A}={(A(i),B(i))}_{iin I}$$A={(A(i),B(i))}i∈I of pairs of spaces with base points $$*_iin B(i)$$∗i∈B(i), there is a definition of the “polyhedral product” $${{mathbf A}^L}$$AL of $${mathbf A}$$A with respect to $$L$$L. Sometimes this is called a “generalized moment angle complex”. This note concerns two refinements to earlier work of the first author. First, when $$L$$L is infinite, the definition of polyhedral product needs clarification. Second, the earlier paper omitted some subtle parts of the necessary and sufficient conditions for polyhedral products to be aspherical. Correct versions of these necessary and sufficient conditions are given in the present paper.