Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-19T10:09:06.621Z Has data issue: false hasContentIssue false
  • English
  • Français

SAMELSON PRODUCTS OF SO(3) AND APPLICATIONS†

Published online by Cambridge University Press:  09 August 2007

YASUHIKO KAMIYAMA ,
DAISUKE KISHIMOTO ,
AKIRA KONO  and
SHUICHI TSUKUDA
YASUHIKO KAMIYAMA
Affiliation:
Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan e-mail: kamiyama@sci.u-ryukyu.ac.jp
DAISUKE KISHIMOTO
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan e-mail: kishi@math.kyoto-u.ac.jp
AKIRA KONO
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan e-mail: kono@math.kyoto-u.ac.jp
SHUICHI TSUKUDA
Affiliation:
Department of Mathematics, University of the Ryukyus, Nishihara-Cho, Okinawa 903-0213, Japan e-mail: tsukuda@math.u-ryukyu.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Certain generalized Samelson products of SO(3) are calculated and applications to the homotopy of gauge groups are given.

Keywords

Primary 55Q15Secondary 55P1554C35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 405 - 409
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

Footnotes

†

Supported by Grant-in-Aid for Scientific Research (B) 18340016.

References

REFERENCES

1. Adams, J. F., Vector fields on spheres, Ann. of Math. 75 (1962), 603–632.CrossRefGoogle Scholar
2. Arkowitz, M., The generalized Whitehead product, Pacific J. Math. 12 (1962), 7–23.CrossRefGoogle Scholar
3. Atiyah, M. F., Thom complexes, Proc. London Math. Soc. (3) 11 (1961), 291–310.CrossRefGoogle Scholar
4. Atiyah, M. F. and Bott, R., The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), 523–615.Google Scholar
5. Bott, R., A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960), 249–256.CrossRefGoogle Scholar
6. Hamanaka, H. and Kono, A., Unstable K1-group and homotopy type of certain gauge groups, Proc. Royal Soc. Edinburgh Sect. A 136 (2006), 149–155.CrossRefGoogle Scholar
7. Kamiyama, Y. and Kishimoto, D., Spin structures on instanton moduli spaces, preprint.Google Scholar
8. Kono, A., A note on the homotopy types of certain gauge groups, Proc. Royal Soc. Edinburgh Sect. A 117 (1991), 295–297.CrossRefGoogle Scholar
9. Lang, G. E., The evaluation map and EHP sequences, Pacific J. Math. 44 (1973), 201–210.CrossRefGoogle Scholar
10. Tsukuda, S., Comparing the homotopy types of the components of (S4, B SU (2)), J. Pure. Appl. Algebra 161 (2001), 235–243.CrossRefGoogle Scholar