Topological space with trivial cup product

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

Definition

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

• Acyclic space
• Sphere
• Suspension space

Metaproperties

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