Fibrations with noncommutative fibers

Abstract

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.

40 pages

References in corpus (3)

• Principal noncommutative torus bundles
• Locally Inner Actions on $C_0(X)$-Algebras
• The structure of crossed products of irrational rotation algebras by finite subgroups of SL_2 (Z)

Cited by in corpus (1)

• T-duality for circle bundles via noncommutative geometry