Topological space with trivial cup product

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This property of topological spaces depends only on the cohomology ring viewed as a graded ring. In particular it is homotopy-invariant


A topological space is said to have 'trivial cup product if for i,j > 0, the cup product between the i^{th} and j^{th} cohomology groups is trivial.

Relation with other properties

Stronger properties



A wedge sum of topological spaces, each with trivial cup product, continues to have trivial cup product.