$E$-Theory is a Special Case of $KK$-Theory

DOI10.1112/S0024611503014436zbMath1045.19001arXivmath/0209088OpenAlexW1982994177MaRDI QIDQ4465103

Klaus Thomsen, Vladimir M. Manuilov

Publication date: 27 May 2004

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209088

zbMATH Keywords

KK-theoryE-theoryasymptotic morphismsConnes-Higson map

Mathematics Subject Classification ID

Ext and (K)-homology (19K33) Kasparov theory ((KK)-theory) (19K35) Categories, functors in functional analysis (46M15)

Related Items (11)

Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture ⋮ The Calkin algebra has outer automorphisms ⋮ Translation invariant asymptotic homomorphisms and extensions of \(C^*\)-algebras ⋮ The Calkin algebra, Kazhdan's property (T), and strongly self‐absorbing C∗$\mathrm{C}^*$‐algebras ⋮ Semi-invertible extensions of \(C^{*}\)-algebras ⋮ On equivalence of two approaches in index theory ⋮ All extensions of \(C^*_r(\mathbb F_n)\) are semi-invertible ⋮ Continuity conditions for finite-dimensional locally bounded representations of connected locally compact groups ⋮ Extensions of the reduced group \(C^{*}\)-algebra of a free product of amenable groups ⋮ Pictures of \(KK\)-theory for real \(C^*\)-algebras and almost commuting matrices ⋮ One more pathology of \(C^{*}\)-algebraic tensor products

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