Stable unextendibility of vector bundles over the quaternionic projective spaces
Hiroshima Mathematical Journal Volume 33 Issue 3
Page 343-357
published_at 2003-11
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| File | |
| Title ( eng ) |
Stable unextendibility of vector bundles over the quaternionic projective spaces
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| Creator | |
| Source Title |
Hiroshima Mathematical Journal
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| 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.
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| Keywords |
vector bundle
extendible
quaternionic projective space
Pontrjagin class
Stiefel-Whitney class
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | departmental bulletin paper |
| Publisher |
Department of Mathematics, Graduate School of Science, Hiroshima University
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| Date of Issued | 2003-11 |
| Publish Type | Version of Record |
| Access Rights | open access |
| Source Identifier |
[ISSN] 0018-2079
[NCID] AA00664323
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