## Homology, Homotopy and Applications

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

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1296223834

**Mathematical Reviews number (MathSciNet)**

MR2721152

**Zentralblatt MATH identifier**

1198.55009

**Subjects**

Primary: 55R50: Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX} 55S05: Primary cohomology operations

**Keywords**

Stiefel-Whitney class vector bundle squaring operation

#### Citation

Tanaka, Ryuichi. On trivialities of Stiefel-Whitney classes of vector bundles over iterated suspension spaces. Homology Homotopy Appl. 12 (2010), no. 1, 357--366. https://projecteuclid.org/euclid.hha/1296223834