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
J. Klein, C. Schochet, and S. Smith, Continuous trace C*-algebras, gauge groups and rational homotopy, Journal of Topology and Analysis 1(3) (2009), 261-288.