Vol. 300, No. 1, 2019

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Homotopy decompositions of the classifying spaces of pointed gauge groups

Stephen Theriault

Vol. 300 (2019), No. 1, 215–231
Abstract

Let G be a topological group and let G(P) be the pointed gauge group of a principal G-bundle P M. We prove that if G is homotopy commutative then the homotopy type of the classifying space BG(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.

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