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Unstable K1-group and homotopy type of certain gauge groups

Published online by Cambridge University Press:  12 July 2007

Hiroaki Hamanaka  and
Akira Kono
Hiroaki Hamanaka
Affiliation:
Department of Natural Science, Hyogo University of Teacher Education Yashiro, Hyogo 673-1494, Japan (hammer@sci.hyogo-u.ac.jp)
Akira Kono
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (kono@math.kyoto-u.ac.jp)
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Abstract

We denote the group of homotopy set [X, U(n)] by the unstable K1-group of X. In this paper, using the unstable K1-group of the multi-suspended CP2, we give a necessary condition for two principal SU(n)-bundles over §4 to have the associated gauge group of the same homotopy type, which is an improvement of the result of Sutherland and, particularly, show the complete classification of homotopy types of SU(3)-gauge groups over S4.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 149 - 155
Copyright
Copyright © Royal Society of Edinburgh 2006

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