We study an analogue of fibrations of topological spaces with the homotopy lifting property in the setting of C*-algebra bundles. We then derive an analogue of the Leray–Serre spectral sequence to compute the K-theory of the fibration in terms of the cohomology of the base and the K-theory of the fibres. We present many examples which show that fibrations with noncommutative fibres appear in abundance in nature.
Cite this article
Siegfried Echterhoff, Ryszard Nest, Hervé Oyono-Oyono, Fibrations with noncommutative fibers. J. Noncommut. Geom. 3 (2009), no. 3, pp. 377–417DOI 10.4171/JNCG/41