Kasparov's bivariant \(K\)-theory and applications

zbMath0746.19008MaRDI QIDQ1177699

Georges Skandalis

Publication date: 26 June 1992

Published in: Expositiones Mathematicae (Search for Journal in Brave)

zbMATH Keywords

survey\(C^*\)-algebraFredholm operators\(KK\)-theoryhomotopy invarianceoperator \(K\)-theoryindex theorems\(K\)-homologyequivariant \(KK\)-theory\(K\)- nuclearityNovikov's conjectureoperators on foliationsquasi-homomorphisms

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Kasparov theory ((KK)-theory) (19K35) Research exposition (monographs, survey articles) pertaining to (K)-theory (19-02)

Related Items (14)

Generalized Connes–Chern characters inKK-theory with an application to weak invariants of topological insulators ⋮ KK-theory of reduced free-product \(C^*\)-algebras ⋮ Differential algebras with Banach-algebra coefficients. I: From \(C^*\)-algebras to the \(K\)-theory of the spectral curve ⋮ A simple separable exact \(C^*\)-algebra not anti-isomorphic to itself ⋮ Topologizing UCTs for unital extensions ⋮ Superconnections, anomalies and non-BPS brane charges ⋮ Quantum Hall conductivity in a Landau type model with a realistic geometry. II ⋮ \(K\)-duality for pseudomanifolds with isolated singularities ⋮ Extensions of the reduced group \(C^{*}\)-algebra of a free product of amenable groups ⋮ An index for gauge-invariant operators and the Dixmier-Douady invariant ⋮ Pseudodifferential operators on manifolds with fibred corners ⋮ The Baum-Connes assembly map, delocalization and the Chern character ⋮ Chern-Simons invariants in \textit{KK}-theory ⋮ Quasidiagonal extensions and sequentially trivial asymptotic homomorphisms

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