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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The power of the tangent bundle of the real projective space, its complexification and extendibility


Authors: Teiichi Kobayashi, Hironori Yamasaki and Toshio Yoshida
Journal: Proc. Amer. Math. Soc. 134 (2006), 303-310
MSC (2000): Primary 55R50; Secondary 55N15
Published electronically: June 13, 2005
MathSciNet review: 2170572
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Abstract: We establish the formulas on the power $\tau^k$ of the tangent bundle $\tau=\tau(RP^n)$ of the real projective $n$-space $RP^n$ and its complexification $c\tau^k$, and apply the formulas to the problem of extendibility and stable extendiblity of $\tau^k$ and $c\tau^k$.


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Additional Information

Teiichi Kobayashi
Affiliation: Department of Mathematics, Faculty of Science, Kochi University, Kochi 780–8520, Japan
Email: kteiichi@lime.ocn.ne.jp

Hironori Yamasaki
Affiliation: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739–8526, Japan
Email: d042710@math.sci.hiroshima-u.ac.jp

Toshio Yoshida
Affiliation: Department of Mathematics, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739–8521, Japan
Email: t-yosida@mis.hiroshima-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07971-2
PII: S 0002-9939(05)07971-2
Keywords: Vector bundle, tangent bundle, real projective space, extendibility, stable extendibility, $KO$-theory, $K$-theory
Received by editor(s): June 1, 2004
Received by editor(s) in revised form: August 30, 2004
Published electronically: June 13, 2005
Communicated by: Paul Goerss
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.