The fine structure of the Kasparov groups. I: Continuity of the KK-pairing

DOI10.1006/jfan.2001.3784zbMath0990.19003arXivmath/0107050OpenAlexW2016115282MaRDI QIDQ5949992

Claude L. Schochet

Publication date: 14 August 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107050

zbMATH Keywords

\(KK\)-theorybivariant \(K\)-theoryKasparov pairingKasparov productpolonais groupquasihomomorphism

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Kasparov theory ((KK)-theory) (19K35)

Related Items

Topologizing UCTs for unital extensions, The Ext-group of unitary equivalence classes of unital extensions, Pseudometrics on Ext-semigroups, An approximate universal coefficient theorem, On the topology of the Kasparov groups and its applications, The fine structure on the Kasparov groups. II: Topologizing the UCT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Abstract Bott periodicity in KK-theory
• Algebraic \(K\)-theory of stable \(C^*\)-algebras
• A new look at KK-theory
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• Topological methods for \(C^*\)-algebras. III: Axiomatic homology
• Topological methods for \(C^*\)-algebras. IV: Mod p homology
• A new description of Kasparov's theory of \(C^*\)-algebra extensions
• Correction to: ``The UCT, the Milnor sequence, and a canonical decomposition of the Kasparov groups
• The topological snake lemma and corona algebras
• The fine structure on the Kasparov groups. II: Topologizing the UCT
• The UCT, the Milnor sequence, and a canonical decomposition of the Kasparov groups
• Morphisms of extensions of \(C^*\)-algebras: Pushing forward the Busby invariant
• Homotopy classes of *-homomorphisms between stable \(C^*\)-algebras and their multiplier algebras
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• Group Extensions and Cohomology for Locally Compact Groups. III
• Extensions of 𝐶*-algebras, operators with compact self-commutators, and 𝐾-homology