#### Document Type

Article

#### Abstract

Let ζ be an *n*-dimensional complex matrix bundle over a compact metric space *X* and let *A*_{ζ} denote 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 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*.

#### Disciplines

Algebra | Analysis | Geometry and Topology

#### Recommended Citation

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.

#### Included in

Algebra Commons, Analysis Commons, Geometry and Topology Commons

## Comments

This is the final accepted manuscript copy, derived from arXiv.org (http://arxiv.org/abs/0811.0771v4), of an electronic version of an article published as

Journal of Topology and Analysis1(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.