The Künneth theorem and the universal coefficient theorem for equivariant 𝐾-theory and 𝐾𝐾-theory

DOI10.1090/memo/0348zbMath0607.46043OpenAlexW4212862131MaRDI QIDQ3746335

Claude L. Schochet, Jonathan M. Rosenberg

Publication date: 1986

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0348

zbMATH Keywords

equivariant K-theoryKünneth formulauniversal coefficient theoremKasparov's KK-theorycoefficient spectral sequencescompact connected Lie group with torsion free fundamental group

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Topological (K)-theory (55N15) Universal coefficient theorems, Bockstein operator (55U20) (K)-theory operations and generalized cohomology operations in algebraic topology (55S25) Homology of a product, Künneth formula (55U25)

Related Items (14)

Equivariant Poincaré duality for quantum group actions ⋮ Crossed products of type I AF algebras by Abelian groups ⋮ A remark on twists and the notion of torsion-free discrete quantum groups ⋮ Equivariant comparison of quantum homogeneous spaces ⋮ Sequentially split ∗-homomorphisms between C*-algebras ⋮ Character formulæ and GKRS multiplets in equivariant \(K\)-theory ⋮ Codimension 2 transfer of higher index invariants ⋮ The Künneth theorem in equivariant \(K\)-theory for actions of a cyclic group of order 2 ⋮ Relative \(K\) homology and \(C^*\) algebras ⋮ Characteristic classes of a \(\Pi\)-algebra and spectral sequences in biinvariant \(K\)-theory. ⋮ A more general method to classify up to equivariant \(KK\)-equivalence ⋮ Higher \(G\)-signatures for Lipschitz manifolds ⋮ Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture ⋮ The bulk–dislocation correspondence for weak topological insulators on screw–dislocated lattices

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