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(n)–bundles.

Keywords
gauge group, mod $p$ decomposition
Mathematical Subject Classification 2010
Primary: 57S05
Secondary: 55R70, 54C35, 55P15
References
Publication
Received: 7 May 2012
Revised: 18 September 2012
Accepted: 1 February 2013
Published: 18 May 2013
Authors
Daisuke Kishimoto
Department of Mathematics
Kyoto University
Kyoto 606-8502
Japan
Akira Kono
Department of Mathematical Science, Faculty of Science and Engineering
Doshisha University
Kyoto 610-0394
Japan
Mitsunobu Tsutaya
Department of Mathematics
Kyoto University
Kyoto 606-8502
Japan