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arXiv · 0811.0771

Continuous trace C*-algebras, gauge groups and rationalization

John R. Klein·Claude L. Schochet·Samuel B. Smith
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Abstract

Let ζbe an n-dimensional complex matrix bundle over a compact metric space X and let A_ζdenote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UA_ζ, the group of unitaries of A_ζ. The answer turns out to be independent of the bundle ζand 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.

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John R. Klein, Claude L. Schochet, Samuel B. Smith. 2009-08-19. Continuous trace C*-algebras, gauge groups and rationalization. https://arxiv.org/abs/0811.0771

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