Continuous trace C*-algebras, gauge groups and rationalization

2008/11/05 by John R. Klein, Klein, John R., Claude L. Schochet +3
Mathematics · #46J05 #46L85 #54C35 #55P15 #55P45 #55P62 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AT #math.KT #msc:46J05 #msc:46L85 #msc:54C35 #msc:55P15 #msc:55P45 #msc:55P62

paper · pdf · doi:10.48550/arxiv.0811.0771

Final version. To appear in J. of Topology and Analysis. Garbled text in abstract removed

arxiv created 2009/08/19 · arxiv updated 2009/12/01

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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