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Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζ denote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.


Algebra | Analysis | Geometry and Topology


This is the final accepted manuscript copy, derived from (, of an electronic version of an article published as Journal of Topology and Analysis 1(3) (2009), 261-288 [DOI: 10.1142/S179352530900014X], © Copyright World Scientific Publishing Company, Journal of Topology and Analysis.

2000 Mathematics Subject Classification: 46J05, 46L85, 55P62, 54C35, 55P15, 55P45.