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A space B is described as W-trivial if for every vector bundle over B, all the Stiefel-Whitney classes vanish. We prove that if B is a 9-fold suspension, then B is W-trivial. We also determine all pairs (k, n) of positive integers for which ΣFP is W-trivial, where F = R,C or H.

On trivialities of Stiefel-Whitney classes of vector bundles over iterated suspension spaces