Oin trivialities of Steifel-Whitney classes of vector bundles over iterated suspensions of Dold manifolds

Abstract

A space $X$ is called $W$-trivial if for every vector bundle $\xi$ over $X$, the total Stiefel-Whitney class $W(\xi) = 1$. In this article we shall investigate whether the suspensions $\Sigma^k D(m,n)$ of Dold manifolds are $W$-trivial or not.