On the homotopy types of Sp(n) gauge groups

Kishimoto, Daisuke; Kono, Akira

doi:10.2140/agt.2019.19.491

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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

DOI: 10.2140/agt.2019.19.491

Abstract

Let $G_{k, n}$ be the gauge group of the principal $Sp (n)$ –bundle over $S^{4}$ corresponding to $k \in ℤ ≅ π_{3} (Sp (n))$ . We refine the result of Sutherland on the homotopy types of $G_{k, n}$ and relate it to the order of a certain Samelson product in $Sp (n)$ . Then we classify the $p$ –local homotopy types of $G_{k, n}$ for ${(p - 1)}^{2} + 1 \geq 2 n$ .

Keywords

gauge group, homotopy type, unstable K–theory

Mathematical Subject Classification 2010

Primary: 54C35, 55P15

References

Publication

Received: 26 April 2018

Revised: 9 July 2018

Accepted: 3 September 2018

Published: 6 February 2019

Authors

Daisuke Kishimoto
Department of Mathematics Kyoto University Kyoto Japan

Akira Kono
Faculty of Science and Engineering Doshisha University Kyoto Japan

Volume 19, issue 1 (2019)