Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

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

Pages: 357 – 366

DOI: http://dx.doi.org/10.4310/HHA.2010.v12.n1.a18


Ryuichi Tanaka (Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)


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 $Σ_kFP_n$ is W-trivial, where $F = \mathbb{R}, \mathbb{C} or \mathbb{H}$.


Stiefel-Whitney class; vector bundle; squaring operation

2010 Mathematics Subject Classification

55R50, 55S05

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Published 1 January 2010