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On p-local homotopy types of gauge groups

Published online by Cambridge University Press:  30 January 2014

Daisuke Kishimoto ,
Akira Kono  and
Mitsunobu Tsutaya
Daisuke Kishimoto
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (kisihi@math.kyoto-u.ac.jp)
Akira Kono
Affiliation:
Department of Mathematical Science, Faculty of Science and Engineering, Doshisha University, Kyoto 610-0394, Japan (akono@mail.doshisha.ac.jp)
Mitsunobu Tsutaya
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan (tsutaya@math.kyoto-u.ac.jp)
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Abstract

The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 1 , February 2014 , pp. 149 - 160
Copyright
Copyright © Royal Society of Edinburgh 2014 

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