Algebraic & Geometric Topology

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

Daisuke Kishimoto and Akira Kono

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Abstract

Let G k , n be the gauge group of the principal Sp ( n ) –bundle over S 4 corresponding to k 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 2 n .

Article information

Source
Algebr. Geom. Topol., Volume 19, Number 1 (2019), 491-502.

Dates
Received: 26 April 2018
Revised: 9 July 2018
Accepted: 3 September 2018
First available in Project Euclid: 12 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.agt/1549940440

Digital Object Identifier
doi:10.2140/agt.2019.19.491

Mathematical Reviews number (MathSciNet)
MR3910588

Zentralblatt MATH identifier
07053581

Subjects
Primary: 54C35: Function spaces [See also 46Exx, 58D15] 55P15: Classification of homotopy type

Keywords
gauge group homotopy type unstable K–theory

Citation

Kishimoto, Daisuke; Kono, Akira. On the homotopy types of $\mathrm{Sp}(n)$ gauge groups. Algebr. Geom. Topol. 19 (2019), no. 1, 491--502. doi:10.2140/agt.2019.19.491. https://projecteuclid.org/euclid.agt/1549940440


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