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On the homotopy types of $\mathrm{Sp}(n)$ gauge groups

Daisuke Kishimoto and Akira Kono

Algebraic & Geometric Topology 19 (2019) 491–502

Let Gk,n be the gauge group of the principal Sp(n)–bundle over S4 corresponding to k π3(Sp(n)). We refine the result of Sutherland on the homotopy types of Gk,n and relate it to the order of a certain Samelson product in Sp(n). Then we classify the p–local homotopy types of Gk,n for (p 1)2 + 1 2n.

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gauge group, homotopy type, unstable K–theory
Mathematical Subject Classification 2010
Primary: 54C35, 55P15
Received: 26 April 2018
Revised: 9 July 2018
Accepted: 3 September 2018
Published: 6 February 2019
Daisuke Kishimoto
Department of Mathematics
Kyoto University
Akira Kono
Faculty of Science and Engineering
Doshisha University