#### Volume 13, issue 3 (2013)

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Mod $p$ decompositions of gauge groups

### Daisuke Kishimoto, Akira Kono and Mitsunobu Tsutaya

Algebraic & Geometric Topology 13 (2013) 1757–1778
##### Abstract

We give mod $p$ decompositions of homotopy types of the gauge groups of principal bundles over spheres, which are compatible with mod $p$ decompositions of Lie groups given by Mimura, Nishida and Toda. As an application, we also give some computations on the homotopy types of gauge groups. In particular, we show the $p$–local converse of the result of Sutherland on the classifications of the gauge groups of principal $SU\left(n\right)$–bundles.

##### Keywords
gauge group, mod $p$ decomposition
##### Mathematical Subject Classification 2010
Primary: 57S05
Secondary: 55R70, 54C35, 55P15