Continuous trace C*-algebras, gauge groups and rationalization

Details Continuous trace C*-algebras, gauge groups and rationalization Continuous trace C*-algebras, gauge groups and rationalization

2008-11-05

arxiv.org/abs/0811.0771v4

Mathematics

Algebraic Topology

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

Scientific paper

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

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