Homotopy decompositions of the classifying spaces of pointed gauge groups

Let $G$ be a topological group and let $G^{*} (P)$ be the pointed gauge group of a principal $G$ -bundle $P \to M$ . We prove that if $G$ is homotopy commutative then the homotopy type of the classifying space $B G^{*} (P)$ can be completely determined for certain $M$ . This also works $p$ -locally, and valid choices of $M$ include closed simply connected four-manifolds when localised at an odd prime $p$ . In this case, an application is to calculate part of the mod- $p$ homology of the classifying space of the full gauge group.

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Keywords

gauge group, mapping space, homotopy type, homology

Mathematical Subject Classification 2010

Primary: 55P15, 55R35

Secondary: 54C35, 81T13

Milestones

Received: 2 March 2017

Revised: 6 August 2018

Accepted: 10 August 2018

Published: 20 July 2019

Authors

Stephen Theriault
Mathematical Sciences University of Southampton Southampton United Kingdom

Vol. 300, No. 1, 2019

Stephen Theriault

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors