Stable unextendibility of vector bundles over the quaternionic projective spaces

Hiroshima Mathematical Journal Volume 33 Issue 3 Page 343-357 published_at 2003-11
アクセス数 : 521
ダウンロード数 : 169

今月のアクセス数 : 0
今月のダウンロード数 : 0
File
HiroshimaMathJ_33_343.pdf 494 KB 種類 : fulltext
Title ( eng )
Stable unextendibility of vector bundles over the quaternionic projective spaces
Creator
Source Title
Hiroshima Mathematical Journal
Volume 33
Issue 3
Start Page 343
End Page 357
Abstract
We study the stable unextendibility of vector bundles over the quaternionic projective space HP^n by making use of combinatorial properties of the Stiefel-Whitney classes and the Pontrjagin classes. First, we show that the tangent bundle of HP^n is not stably extendible to HP^<n+1> for n ≥ 2, and also induce such a result for the normal bundle associated to an immersion of HP^n into R^<4n+k>. Secondly, we show a sufficient condition for a quaternionic r-dimensional vector bundle over HP^n not to be stably extendible to HP^<n+l> for r ≤ n and l > 0, which is also a necessary condition when r = n and l = 1.
Keywords
vector bundle
extendible
quaternionic projective space
Pontrjagin class
Stiefel-Whitney class
NDC
Mathematics [ 410 ]
Language
eng
Resource Type departmental bulletin paper
Publisher
Department of Mathematics, Graduate School of Science, Hiroshima University
Date of Issued 2003-11
Publish Type Version of Record
Access Rights open access
Source Identifier
[ISSN] 0018-2079
[NCID] AA00664323