Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-30T23:39:08.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Function spaces related to gauge groups

Published online by Cambridge University Press:  14 November 2011

W. A. Sutherland
W. A. Sutherland
Affiliation:
New College, Oxford OX1 3BN, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Components in the function space of maps from a space X to the classifying space BG of a topological group G can sometimes be distinguished up to homotopy type by a Samelson product method. When X is a closed Riemann surface and G is a unitary group, this method is nearly sufficient to classify the components up to homotopy type.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 185 - 190
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Atiyah, M. F. and Bott, R.. The Yang-Mills equations over Riemann surfaces. Proc. Roy. Soc. London Ser. A 308 (1982), 523–615.Google Scholar
2Booth, P., Heath, P., Morgan, C. and Piccinini, R.. Remarks on the homotopy type of groups of gauge transformations. C. R. Math. Acad. Sci. Canada 3 (1981), 3–6.Google Scholar
3Bott, R.. A note on the Samelson product in the Classical Groups. Comment. Math. Helv. 34 (1960), 249–256.CrossRefGoogle Scholar
4Bousfield, A. K. and Kan, D. M.. Homotopy limits, completions and localizations. Lecture Notes in Mathematics 304 (Berlin: Springer, 1972).Google Scholar
5Crabb, M. C. and Sutherland, W. A.. Functions spaces and Hunvitz-Radon numbers. Math. Scand. 55 (1984), 67–90.CrossRefGoogle Scholar
6Hilton, P., Mislin, G. and Roitberg, J.. Localization of Nilpotent groups and spaces (Amsterdam: North Holland, 1975).Google Scholar
7Gottlieb, D. H.. Applications of bundle map theory. Trans. Amer. Math. Soc. 7 (1972), 23–50.CrossRefGoogle Scholar
8Kono, A.. A note on the homotopy type of certain gauge groups. Proc. Roy. Soc. Edinburgh Sect. A 117 (1991), 295–297.Google Scholar
9Masbaum, G.. Sur l'algèbre de cohomologie entière du classifiant du groupe de jauge. C. R. Acad. Sci. Paris 307 (1) (1988), 339–342.Google Scholar
10Masbaum, G.. Sur la cohomologie due classificant du groupe de jauge sur certains 4-complexes. C. R. Acad. Sci. Paris 310 (1) (1990), 115–118.Google Scholar
11Singer, I. M.. Some remarks on the Gribov ambiguity. Comm. Math. Phys. 60 (1978), 7–12.Google Scholar
12Sullivan, D.. Geometric Topology, part I (Mimeo notes, M.I.T., 1970).Google Scholar
13Whitehead, G. W.. On products in homotopy groups. Ann. Math. 47 (1946), 460–475.Google Scholar
14Whitehead, J. H. C.. On certain theorems of G. W. Whitehead. Ann. Math. 58 (1953), 418–428.Google Scholar