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Homotopy decompositions of gauge groups over real surfaces

Michael West

Algebraic & Geometric Topology 17 (2017) 2429–2480
Abstract

We analyse the homotopy types of gauge groups of principal U(n)–bundles associated to pseudoreal vector bundles in the sense of Atiyah. We provide satisfactory homotopy decompositions of these gauge groups into factors in which the homotopy groups are well known. Therefore, we substantially build upon the low-dimensional homotopy groups as provided by Biswas, Huisman and Hurtubise.

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Keywords
homotopy types, homotopy groups of special spaces, classification of homotopy types
Mathematical Subject Classification 2010
Primary: 55P15, 55Q52
Secondary: 30F50
References
Publication
Received: 20 June 2016
Revised: 2 November 2016
Accepted: 29 November 2016
Published: 3 August 2017
Authors
Michael West
University of Southampton
Building 54
Salisbury Rd
Southampton
SO17 1BJ
United Kingdom