Cohomology of $S^2\times S^2/\mathbb{Z}_2$
I was looking at this question, the accepted answer uses the homology of the space to find the cohomology. I was wondering how one could compute the homology of an orbit space like this in the first place?
"The product of two spheres admits a diagonal $ℤ_2$ action, $(x, y)\mapsto(−x,−y)$" - describe the homology groups of the orbit space of this free action.