Fiberwise KK-equivalence of continuous fields of C*-algebras

DOI10.1017/is008001012jkt041zbMath1173.46050arXivmath/0611408OpenAlexW2110264124MaRDI QIDQ3628701

Marius Dǎdǎrlat

Publication date: 20 May 2009

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611408

zbMATH Keywords

\(K\)-theoryKirchberg algebrasCuntz algebrascontinuous fields

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Classifications of (C^*)-algebras (46L35) Kasparov theory ((KK)-theory) (19K35)

Related Items (13)

A Dixmier-Douady theory for strongly self-absorbing \(C^\ast\)-algebras ⋮ Fibrations with noncommutative fibers ⋮ E-theory for C[0, 1-algebras with finitely many singular points] ⋮ Equivariant Kirchberg-Phillips-type absorption for amenable group actions ⋮ E-theory for \(C^*\)-algebras over topological spaces ⋮ Nuclear dimension and 𝒵-stability of non-simple 𝒞*-algebras ⋮ Rokhlin dimension: duality, tracial properties, and crossed products ⋮ A new proof of Kirchberg's \(\mathcal{O}_2\)-stable classification ⋮ A topological invariant for continuous fields of Cuntz algebras ⋮ Continuous fields of \(C^*\)-algebras over finite dimensional spaces ⋮ Rokhlin actions of finite groups on UHF-absorbing $\mathrm {C}^*$-algebras ⋮ One-parameter continuous fields of Kirchberg algebras with rational $K$-theory ⋮ A topological invariant for continuous fields of Cuntz algebras II

Cites Work

• Infinite non-simple \(C\)*-algebras: absorbing the Cuntz algebra \({\mathcal O}_\infty\)
• The structure of algebras of operator fields
• The Baum-Connes conjecture via localisation of categories
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• Equivariant KK-theory and the Novikov conjecture
• K-theory for certain C*-algebras
• The Baum-Connes conjecture for amenable foliations
• Quasidiagonal morphisms and homotopy
• \(RKK(X)\)-nuclearity (after G. Skandalis)
• Non-simple purely infinite \(C^{*}\)-algebras: The Hausdorff case.
• The UCT, the Milnor sequence, and a canonical decomposition of the Kasparov groups
• Continuous fields of Kirchberg \(C^*\)-algebras
• Strongly self-absorbing $C^{*}$-algebras
• Non-simple purely infinite C*-algebras

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