## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 36, Number 3 (2006), 339-351.

### Stable extendibility of the tangent bundles over lens spaces

Mitsunori Imaoka and Hironori Yamasaki

#### Abstract

The purpose of this paper is to study the stable extendibility of the tangent bundle $\tau_n(p)$ of the $(2n+1)$-\hspace dimensional standard lens space $\mL^n(p)$ for odd prime $p$. We investigate the value of integer $m$ for which $\tau_n(p)$ is stably extendible to $\mL^m(p)$ but not stably extendible to $\mL^{m+1}(p)$, and in particular we completely determine $m$ for $p=5$ or $7$. A stable splitting of $\tau_n(p)$ and the stable extendibility of a Whitney sum of $\tau_n(p)$ are also discussed.

#### Article information

**Source**

Hiroshima Math. J., Volume 36, Number 3 (2006), 339-351.

**Dates**

First available in Project Euclid: 13 February 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1171377077

**Digital Object Identifier**

doi:10.32917/hmj/1171377077

**Mathematical Reviews number (MathSciNet)**

MR2290661

**Zentralblatt MATH identifier**

1140.55011

**Subjects**

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

Secondary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}

**Keywords**

Tangent bundle lens space stably extendible KO-theory

#### Citation

Imaoka, Mitsunori; Yamasaki, Hironori. Stable extendibility of the tangent bundles over lens spaces. Hiroshima Math. J. 36 (2006), no. 3, 339--351. doi:10.32917/hmj/1171377077. https://projecteuclid.org/euclid.hmj/1171377077