Elsevier

Topology and its Applications

Volume 156, Issue 2, 1 December 2008, Pages 268-273
Topology and its Applications

Stable extendibility of vector bundles over RPn and the stable splitting problem

https://doi.org/10.1016/j.topol.2008.07.006Get rights and content
Under an Elsevier user license
open archive

Abstract

Let F be the real number field R or the complex number field C, and let RPn denote the real projective n-space. In this paper, we study the conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m>n, and establish the formulas on the power ζr=ζζ (r-fold) of an F-vector bundle ζ over RPn. Our results are improvements of the previous papers [T. Kobayashi, H. Yamasaki, T. Yoshida, The power of the tangent bundle of the real projective space, its complexification and extendibility, Proc. Amer. Math. Soc. 134 (2005) 303–310] and [Y. Hemmi, T. Kobayashi, Min Lwin Oo, The power of the normal bundle associated to an immersion of RPn, its complexification and extendibility, Hiroshima Math. J. 37 (2007) 101–109]. Furthermore, we answer the stable splitting problem for F-vector bundles over RPn by means of arithmetic conditions.

MSC

primary
55R50
secondary
55N15

Keywords

Vector bundle
Stably extendible
Extendible
Real projective space
Power of vector bundle
Tensor product
KO-theory
K-theory

Cited by (0)