The cohomology algebra of polyhedral product spaces

2012/06/28 by Qibing Zheng, Zheng, Qibing
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.1206.6629

Abstract

In this paper, we compute the cohomology ring of all homology split polyhedral product spaces and the cohomology algebra over a field of all polyhedral product spaces. As an application, we give two polyhedral product spaces such that all the cohomology homomorphisms induced by inclusion map are the same, but the cohomology rings of the two polyhedral product spaces are not isomorphic.

Related

• The Cohomology Algebra of Polyhedral Product Objects
• A Cartan formula for the cohomology of polyhedral products and its application to the ring structure
• Symmetric Products and a Cartan-type formula for polyhedral products
• On the cohomology of polyhedral products with space pairs (D¹, S⁰)
• The Complement of Polyhedral Product Spaces and the Dual Simplicial Complexes