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

Ryuichi Tanaka

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 Σ^kFPⁿ is W-trivial, where F=R, C or H.

Homology, Homotopy and Applications, Vol. 12 (2010), No. 1, pp.357-366.

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