The Cohomology Algebra of Polyhedral Product Objects
The Cohomology Algebra of Polyhedral Product Objects
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DOI：
10.1016/j.jpaa.2016.05.003
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
Qibing Zheng
中科院分区：
文献类型：
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作者：
Qibing Zheng
本文计算了同调分裂多面体积空间的积分奇异上同调环和多面体积空间域上的奇异上同调代数。作为一个应用，我们给出了两个多面体积空间Z （K; x1, a1）和Z (K; x2, a2)，使得包含引起的上同态同态是相同的，但这两个多面体积空间的上同态环不是同构的。
In this paper, we compute the integral singular cohomology ring of homology split polyhedral product spaces and the singular cohomology algebra over a field of polyhedral product spaces. As an application, we give two polyhedral product spaces Z (K; X 1, A 1) and Z (K; X 2, A 2) such that the cohomology homomorphisms i k⁎: H⁎(X k)→ H⁎(A k) induced by the inclusions are the same, but the cohomology rings of the two polyhedral product spaces are not isomorphic.