Künneth theorem
= Künneth theorem
{c}
{wiki=Künneth_theorem}
The Künneth theorem computes the homology or cohomology of a product from those of its factors. Over a field $k$, $H^*(X\times Y;k)\cong H^*(X;k)\otimes_kH^*(Y;k)$ as graded rings under suitable finiteness hypotheses.