Algebraic & Geometric Topology

Mod $p$ decompositions of gauge groups

Daisuke Kishimoto, Akira Kono, and Mitsunobu Tsutaya

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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.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1757-1778.

Dates
Received: 7 May 2012
Revised: 18 September 2012
Accepted: 1 February 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715599

Digital Object Identifier
doi:10.2140/agt.2013.13.1757

Mathematical Reviews number (MathSciNet)
MR3071142

Zentralblatt MATH identifier
1276.57036

Subjects
Primary: 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
Secondary: 55R70: Fibrewise topology 54C35: Function spaces [See also 46Exx, 58D15] 55P15: Classification of homotopy type

Keywords
gauge group mod $p$ decomposition

Citation

Kishimoto, Daisuke; Kono, Akira; Tsutaya, Mitsunobu. Mod $p$ decompositions of gauge groups. Algebr. Geom. Topol. 13 (2013), no. 3, 1757--1778. doi:10.2140/agt.2013.13.1757. https://projecteuclid.org/euclid.agt/1513715599


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