The cohomology algebra of polyhedral product spaces

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;X1,A1) and Z(K;X2,A2) such that the cohomology homom...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2016-11, Vol.220 (11), p.3752-3776
Main Author: Zheng, Qibing
Format: Article
Language:English
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Summary: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;X1,A1) and Z(K;X2,A2) such that the cohomology homomorphisms ik⁎:H⁎(Xk)→H⁎(Ak) induced by the inclusions are the same, but the cohomology rings of the two polyhedral product spaces are not isomorphic.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2016.05.003