Homotopy Decompositions of Gauge Groups over Real Surfaces

TL;DR

This paper investigates the homotopy types of gauge groups linked to pseudo Real vector bundles over real surfaces, providing decompositions into well-understood factors to advance the understanding of their topological structure.

Contribution

It offers new homotopy decompositions of gauge groups over real surfaces, building upon and extending previous low-dimensional homotopy group results.

Findings

Homotopy decompositions into known factors

Extension of low-dimensional homotopy group results

Enhanced understanding of gauge group topology

Abstract

We analyse the homotopy types of gauge groups of principal U(n)-bundles associated to pseudo Real 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 in a paper by I. Biswas, J. Huisman, and J. Hurtubise.