On continuous maps between Grassmann manifolds (Q1182592)

Let \(G_{n,k}\) \((\widetilde {G}_{n,k})\) denote the Grassmann manifold of \(k\)-planes (resp. oriented \(k\)-planes) in \(\mathbb{R}^ n\). The authors first give results on the nature of the induced map \(f^*: H^*(G_{n,1},\mathbb{Z}_ 2)\to H^*(G_{n,k};\mathbb{Z}_ 2)\) on \(\mathbb{Z}_ 2\)-cohomology for any continuous map \(f: G_{n,k}\to G_{n,l}\). These results, among others, are then used to show the existence resp. the non- existence of equivariant maps \(\widetilde {G}_{n,k}\to \widetilde {G}_{m,p}\) in certain cases depending on the form of, and on various relationships among, the \(n\), \(m\), \(k\), \(p\). The paper concludes with some results on Spans.