An analogue of Serre fibrations for $C^*$-algebra bundles

Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve

doi:10.2969/aspm/05510209

VOL. 55 | 2009 An analogue of Serre fibrations for $C^*$-algebra bundles

Chapter Author(s) Siegfried Echterhoff, Ryszard Nest, Herve Oyono-Oyono

Editor(s) Jean-Pierre Bourguignon, Motoko Kotani, Yoshiaki Maeda, Nobuyuki Tose

Adv. Stud. Pure Math., 2009: 209-221 (2009) DOI: 10.2969/aspm/05510209

Abstract

We study an analogue of Serre fibrations in the setting of $C^*$-algebra bundles. We derive in this framework a Leray–Serre type spectral sequence. We investigate a class of examples which generalise on one hand principal bundles with a $n$-torus as structural group and on the other hand non-commutative tori.