arXiv Analytics

Sign in

arXiv:0811.0771 [math.AT]AbstractReferencesReviewsResources

Continuous trace C*-algebras, gauge groups and rationalization

John R. Klein, Claude L. Schochet, Samuel B. Smith

Published 2008-11-05, updated 2009-08-19Version 4

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.

Comments: Final version. To appear in J. of Topology and Analysis. Garbled text in abstract removed
Categories: math.AT, math.KT
Subjects: 46J05, 46L85, 55P62, 54C35, 55P15, 55P45
Related articles: Most relevant | Search more
arXiv:2204.08867 [math.AT] (Published 2022-04-19)
The homotopy types of $Sp(n)$-gauge groups over $S^{4m}$
arXiv:1909.04643 [math.AT] (Published 2019-09-10)
The Homotopy Types of $SU(4)$-Gauge Groups
arXiv:math/0311313 [math.AT] (Published 2003-11-18)
The rational topology of gauge groups and of spaces of connections

Links

Toolbox