## Homology, Homotopy and Applications

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

Ryuichi Tanaka

#### 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 $\mathbb{H}$.

#### Article information

Source
Homology Homotopy Appl., Volume 12, Number 1 (2010), 357-366.

Dates
First available in Project Euclid: 28 January 2011