On KO-groups of complex Milnor manifolds

Abstract

In this article, we compute the KO -groups of complex Milnor manifold Hr,s. We describe a set of generators for the group KO˜−k(Hr,s). Using this description of generators, we determine which iterated suspensions ΣkHr,s have the property that every vector bundle over it has trivial Steifel-Whitney class.