Relative \(K\) homology and \(C^*\) algebras

DOI10.1007/BF00538877zbMath0755.46035MaRDI QIDQ1181243

Ronald G. Douglas, Paul F. Baum

Publication date: 27 June 1992

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

zbMATH Keywords

Toeplitz operatorselliptic differential operators\(*\)-representationsclosed two-sided idealKasparov groupsanalytic \(K\) homologyfive term exact sequencehomotopy-isomorphic equivalence classesrelative \(K\)-homology groupseparable nuclear \(C^*\) algebra with unittopological \(K\) homology

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Ext and (K)-homology (19K33) Kasparov theory ((KK)-theory) (19K35)

Related Items (11)

An analytic Grothendieck Riemann Roch theorem ⋮ Geometric K-homology with coefficients I: ℤ/kℤ-cycles and Bockstein sequence ⋮ Asymptotic Lipschitz cohomology and higher signatures ⋮ Classification of \(C^*\)-algebras of real rank zero and unsuspended \(E\)-equivalence types ⋮ Relative k-cycles and local elliptic boundary conditions ⋮ Relative \(K\)-homology and \(K\)-homology of an ideal ⋮ Analytic \(K\)-theory on manifolds with corners ⋮ Limit sets as examples in noncommutative geometry ⋮ Boundaries, spectral triples and \(K\)-homology ⋮ Traces of Commutators of Integral Operators – the Aftermath ⋮ Geometric K-homology with coefficients II: The Analytic Theory and Isomorphism

Cites Work

• Faisceaux algébriques cohérents
• Cycles and relative cycles in analytic K-homology
• Algebraic \(K\)-theory of stable \(C^*\)-algebras
• A characterization of KK-theory
• Riemann-Roch and topological K-theory for singular varieties
• Analytic \(K\)-theory on manifolds with corners
• Riemann-Roch for singular varieties
• Extensions of \(C^*\)-algebras and \(K\)-homology
• On the index of Toeplitz operators of several complex variables
• Boundary problems for pseudo-differential operators
• Stability of \(C^ \infty\) mappings. V: Transversality
• Homology theory for locally compact spaces
• Le théorème de Riemann-Roch
• The Künneth theorem and the universal coefficient theorem for equivariant 𝐾-theory and 𝐾𝐾-theory
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• Triangulation of Stratified Objects
• On the Calkin Algebra and the Covering Homotopy Property
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