Kyoto Journal of Mathematics

Refined gauge group decompositions

D. Kishimoto, A. Kono, and S. Theriault

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let G be a simply connected, compact Lie group, let PS4 be a principal G-bundle, and let G(P) be the gauge group of this bundle. When G is a matrix group and p is an odd prime, we use new methods to improve on the p-local homotopy decompositions of G(P) appearing in separate work of the first two authors and the third author.

Article information

Kyoto J. Math., Volume 54, Number 3 (2014), 679-691.

First available in Project Euclid: 14 August 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P35: Loop spaces
Secondary: 54C35: Function spaces [See also 46Exx, 58D15] 81T13: Yang-Mills and other gauge theories [See also 53C07, 58E15]


Kishimoto, D.; Kono, A.; Theriault, S. Refined gauge group decompositions. Kyoto J. Math. 54 (2014), no. 3, 679--691. doi:10.1215/21562261-2693487.

Export citation


  • [B] R. Bott, A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960), 249–256.
  • [BMW] C. P. Boyer, B. M. Mann, and D. Waggonner, On the homology of $\operatorname{SU} (n)$ instantons, Trans. Amer. Math. Soc. 323 (1991), no. 2, 529–561.
  • [G] D. H. Gottlieb, Applications of bundle map theory, Trans. Amer. Math. Soc. 171 (1972), 23–50.
  • [HK] H. Hamanaka and A. Kono, Unstable $K^{1}$-group and homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), 149–155.
  • [H] B. Harris, On the homotopy groups of the classical groups, Ann. of Math. (2) 74 (1961), 407–413.
  • [Ki] D. Kishimoto, Generating varieties, Bott periodicity and instantons, Topology Appl. 157 (2010), 657–668.
  • [KK] D. Kishimoto and A. Kono, Note on mod-$p$ decompositions of gauge groups, Proc. Japan Acad. Ser. A. Math. Sci. 86 (2010), 15–17.
  • [KKT] D. Kishimoto, A. Kono, and M. Tsutaya, Mod-$p$ decompositions of gauge groups, Algebr. Geom. Topol. 13 (2013), 1757–1778.
  • [Ko] A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991), 295–297.
  • [L] G. E. Lang, The evaluation map and $EHP$ sequences, Pacific J. Math. 44 (1973), 201–210.
  • [MNT] M. Mimura, G. Nishida, and H. Toda, Mod-$p$ decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977/78), 627–680.
  • [T1] S. D. Theriault, Odd primary decompositions of gauge groups, Algebr. Geom. Topol. 10 (2010), 535–564.
  • [T2] S.D. Theriault, The homotopy types of $\operatorname{Sp} (2)$-gauge groups, Kyoto J. Math. 50 2010, 591–605.