Mod p decompositions of gauge groups

Kishimoto, Daisuke; Kono, Akira; Tsutaya, Mitsunobu

doi:10.2140/agt.2013.13.1757

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Mod $p$ decompositions of gauge groups

Daisuke Kishimoto, Akira Kono and Mitsunobu Tsutaya

Algebraic & Geometric Topology 13 (2013) 1757–1778

DOI: 10.2140/agt.2013.13.1757

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

Volume 13, issue 3 (2013)