The cohomology algebra of polyhedral product spaces
Qibing Zheng

TL;DR
This paper computes the cohomology algebra of polyhedral product spaces, revealing that similar cohomology homomorphisms can correspond to non-isomorphic cohomology rings, thus highlighting subtle algebraic distinctions.
Contribution
It provides explicit calculations of the cohomology algebra for all homology split polyhedral product spaces and demonstrates non-isomorphic cohomology rings with identical induced homomorphisms.
Findings
Cohomology rings of polyhedral product spaces are explicitly computed.
Identifies cases where cohomology homomorphisms are identical but rings are not isomorphic.
Highlights subtle differences in algebraic structures of polyhedral product spaces.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Commutative Algebra and Its Applications
