Fibrations with noncommutative fibers

2008/10/01 by Siegfried Echterhoff, Echterhoff, Siegfried, Ryszard Nest +4 · 2 citations
Mathematics · #19K35 #46L55 #46L80 #46L85 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:19K35 #msc:46L55 #msc:46L80 #msc:46L85

paper · pdf · doi:10.48550/arxiv.0810.0118

40 pages

arxiv created 2008/10/01 · openalex publication_date 2008/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The structure of crossed products of irrational rotation algebras by finite subgroups of SL₂ (Z)
• Locally Inner Actions on C₀(X)-Algebras

Cited by

• Chern character for torsion-free ample groupoids
• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective

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