Abstract
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 $\Sigma^k F P^n$ is W-trivial, where $F=\mathbb{R}, \mathbb{C}$ or $\mathbb{H}$.
Citation
Ryuichi Tanaka. "On trivialities of Stiefel-Whitney classes of vector bundles over iterated suspension spaces." Homology Homotopy Appl. 12 (1) 357 - 366, 2010.
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