Continuous Trace C*-Algebras, Gauge Groups and Rationalization

Authors

John R. Klein, Wayne State University
Claude Schochet, Wayne State UniversityFollow
Samuel B. Smith, Saint Joseph's University

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

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 Analysis 1(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.

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.