The UCT, the Milnor sequence, and a canonical decomposition of the Kasparov groups

DOI10.1007/BF00534888zbMath0839.19004OpenAlexW2158872848MaRDI QIDQ1908233

Claude L. Schochet

Publication date: 20 March 1996

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

Full work available at URL: https://doi.org/10.1007/bf00534888

zbMATH Keywords

\(KK\)-theoryuniversal coefficient theoremMilnor sequenceseparable nuclear \(C^*\)-algebrasKasparaov groups

Mathematics Subject Classification ID

Noncommutative topology (46L85) (K)-theory and operator algebras (including cyclic theory) (46L80) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Classifications of (C^*)-algebras (46L35) Kasparov theory ((KK)-theory) (19K35) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Topological (K)-theory (55N15) Universal coefficient theorems, Bockstein operator (55U20)

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A universal multicoefficient theorem for the Kasparov groups, Gorenstein homological algebra and universal coefficient theorems, Atiyah-Jänich theorem for \(\sigma\)-\(C^*\)-algebras, On Specht's theorem in UHF \(C^\ast \)-algebras, Spanier–Whitehead K-duality for C∗-algebras, When must pure extensions of countable abelian groups necessarily split?, The fine structure of the Kasparov groups. I: Continuity of the KK-pairing, Fiberwise KK-equivalence of continuous fields of C*-algebras, A CLASSIFICATION OF NON-SIMPLE C*-ALGEBRAS OF TRACIAL RANK ONE: INDUCTIVE LIMITS OF FINITE DIRECT SUMS OF SIMPLE TAI C*-ALGEBRAS, Finite group actions on \(C^{*}\)-algebras with the Rohlin property. II, The fine structure on the Kasparov groups. II: Topologizing the UCT

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