|
The power of the tangent bundle of the real projective space, its complexification and extendibility
Author(s):
Teiichi
Kobayashi;
Hironori
Yamasaki;
Toshio
Yoshida
Journal:
Proc. Amer. Math. Soc.
134
(2006),
303-310.
MSC (2000):
Primary 55R50;
Secondary 55N15
Posted:
June 13, 2005
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We establish the formulas on the power  of the tangent bundle  of the real projective  -space  and its complexification  , and apply the formulas to the problem of extendibility and stable extendiblity of  and  .
References:
-
- 1.
- J. F. Adams, Vector fields on spheres, Ann. of Math. 75 (1962), 603-632. MR 0139178 (25:2614)
- 2.
- D. Husemoller, Fibre bundles, Second edition, Graduate Texts in Mathmatics 20, Springer-Verlag, New York-Hiderberg-Berlin, 1975. MR 0370578 (51:6805)
- 3.
- M. Imaoka and K. Kuwana, Stably extendible vector bundles over the quaternionic projective spaces, Hiroshima Math. J. 29 (1999), 273-279.MR 1704248 (2000h:55027)
- 4.
- T. Kobayashi and K. Komatsu, Extendiblity and stable extendibility of vector bundles over real projective spaces, Hiroshima Math. J. 31 (2001), 99-106. MR 1820697 (2001j:55018)
- 5.
- T. Kobayashi and T. Yoshida, Extendible and stably extendible vector bundles over real projective spaces, J. Math. Soc. Japan 55 (2003), 1053-1059. MR 2003759 (2004i:55022)
- 6.
- T. Kobayashi, H. Maki and T. Yoshida, Remarks on extendible vector bundles over lens spaces and real projective spaces, Hiroshima Math. J. 5 (1975), 487-497. MR 0385857 (52:6716)
- 7.
- T. Kobayashi, H. Maki and T. Yoshida, Extendiblity with degree
 of the complex vector bundles over lens spaces and projective spaces, Mem. Fac. Sci Kochi Univ. (Math.) 1 (1980), 23-33. MR 0561386 (81c:55027) - 8.
- T. Kobayashi, H. Maki and T. Yoshida, Stably extendible vector bundles over the real projective spaces and the lens spaces, Hiroshima Math. J. 29 (1999), 631-638. MR 1728614 (2000k:55023)
- 9.
- R. L. E. Schwarzenberger, Extendible vector bundles over real projective space, Quart. J. Math. Oxford (2) 17 (1966), 19-21. MR 0195105 (33:3310)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
55R50,
55N15
Retrieve articles in all Journals with MSC
(2000):
55R50,
55N15
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:
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
Posted:
June 13, 2005
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org