Relations among generalized characteristic classes
In Topology 3, Suppl. 1, 39-82 (1964; Zbl 0137.427), \textit{E. H. Brown} and \textit{F. P. Peterson} determined the elements of \(H^*(BO;{\mathbb{Z}}/2)\) which vanish on the normal bundles of all n-manifolds. This paper generalizes their result by replacing BO by the classifying space B associated to a class of manifolds and by replacing \(H^*(-;{\mathbb{Z}}/2)\) by a generalized cohomology theory \(E^*\) satisfying some mild orientability conditions. The main general result reduces the determination of these classes to consideration of a stabilization map and a switch map. It is shown that this very general result reduces to Brown and Peterson's in the classical case, and an explicit calculation is made when \(B=BU\) and E is the Morava K-theory K(m).
scientific article; zbMATH DE number 4201172