Geometric realization of Adams maps
This paper considers certain maps on the rational cohomology rings of homogeneous spaces and asks when they are realized by a map of the underlying space. Let \(G\) be a compact, connected Lie group, \(P\) a connected subgroup of equal rank, and let \(l_k\) be the Adams map on \(H^*(G/P;{\mathbb Q})\) which, in degree \(2i\), is multiplication by the integer \(k^i\). It is shown that if \(k\) is prime to the order of the Weyl group of \(G\), then \(l_k\) can be realized by a continuous function. Some examples of non-realizability are given in cases where this coprimality hypothesis does not hold.
scientific article; zbMATH DE number 5912902