## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 37, Number 1 (2007), 45-60.

### Extendibility, stable extendibility and span of some vector bundles over lens spaces mod 3

Teiichi Kobayashi and Kazushi Komatsu

#### Abstract

Let $L^{n}(3)$ be the $(2n+1)$-dimensional standard lens space mod 3 and let $\nu$ denote the normal bundle associated to an immersion of $L^{n}(3)$ in the Euclidean $(4n+3)$-space. In this paper we obtain a theorem on stable unextendibility of $R$-vector bundles over $L^{n}(3)$ improving some results in *Extendibility and stable extendibility of vector bundles over lens spaces* and *Stable extendibility of normal bundles associated to immersions of real projective spaces and lens spaces*, and study relations between stable extendibility and span of vector bundles over $L^{n}(3)$. Furtheremore, we prove that $c\nu$ is extendible to $L^{m}(3)$ for every $m > n$ if and only if $0 \leq n \leq 5$, and prove that $c(\nu \otimes \nu)$ is extendible to $L^{m}(3)$ for every $m > n$ if and only if $0 \leq n \leq 13$ or $n = 15$, where $c$ stands for the complexification and $\otimes$ denotes the tensor product.

#### Article information

**Source**

Hiroshima Math. J., Volume 37, Number 1 (2007), 45-60.

**Dates**

First available in Project Euclid: 11 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1176324094

**Digital Object Identifier**

doi:10.32917/hmj/1176324094

**Mathematical Reviews number (MathSciNet)**

MR2308523

**Zentralblatt MATH identifier**

1141.55010

**Subjects**

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

Secondary: 57R42: Immersions

**Keywords**

Extendible stably extendible span tensor product immersion normal bundle $KO$-theory $K$-theory lens space

#### Citation

Kobayashi, Teiichi; Komatsu, Kazushi. Extendibility, stable extendibility and span of some vector bundles over lens spaces mod 3. Hiroshima Math. J. 37 (2007), no. 1, 45--60. doi:10.32917/hmj/1176324094. https://projecteuclid.org/euclid.hmj/1176324094