Fibrations with non commutative fibers

Siegfried Echteroff (1) , Ryszard Nest (2) , Hervé Oyono-Oyono (3)

1 Mathematishes Institut
2 Department of Mathematical Sciences [Copenhagen]
3 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Noncommutative fibrations; Noncommutative principal torus bundles; K-theory; Leray-Serre spectral sequence

Domaines: Algèbres d'opérateurs [math.OA]

Siegfried Echteroff, Ryszard Nest, Hervé Oyono-Oyono. Fibrations with non commutative fibers. Journal of Noncommutative Geometry, 2009, 3, pp.377-417. ⟨hal-00483033⟩