On stability of non-domination under taking products (Q2796744)

If \(M\) and \(N\) are closed oriented manifolds one says that \(M\) dominates \(N\), writing \(M \geq N\), if there exists a continuous map \(f : M \rightarrow N\) of non-zero degree. The induced map on cohomology in this case is known to be an injection on rational cohomology. This paper obtains results on the (non)existence of domination when the manifold \(N\) is not dominated by a product. Typical of the results is that if \(N\) is not dominated by a product then one has \(M \;\times \;W \geq N \;\times \;W\) if and only if \(M \geq N\).