# Kunneth formula for cohomology

From Topospaces

## Statement

Suppose and are topological spaces. We then have the following relation betwen the cohomology groups of , , and the product space .

For any and any module over a principal ideal domain , we have:

Here, is torsion of modules over the ring .

## Particular cases

### Case of free modules

If all the cohomology groups are free (or more generally, torsion-free) modules over , *and/or* all the cohomology groups are free (or more generally, torsion-free) modules over , then all the torsion part vanishes and we simply get: