\(K\)-homology of \(C^*\)-categories and symmetric spectra representing \(K\)-homology

DOI10.1007/s00208-003-0426-9zbMath1048.19005OpenAlexW1977506244MaRDI QIDQ1434231

Michael Joachim

Publication date: 7 July 2004

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-003-0426-9

zbMATH Keywords

K-theoryBaum-Connes conjecturesymmetric spectraC*-algebrasC*-categories

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Kasparov theory ((KK)-theory) (19K35) Categories, functors in functional analysis (46M15) Spectra with additional structure ((E_infty), (A_infty), ring spectra, etc.) (55P43)

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Localization of cofibration categories and groupoid \(C^\ast\)-algebras ⋮ Morita homotopy theory of \(\mathrm{C}^\ast\)-categories ⋮ L‐theory of C∗$C^*$‐algebras ⋮ Homotopical and operator algebraic twisted \(K\)-theory ⋮ Isomorphism conjectures with proper coefficients ⋮ \(K\)-theory for topological algebroids ⋮ On the relation between K- and L-theory of \(C^*\)-algebras ⋮ Bredon homology and equivariant \(K\)-homology of \(\mathrm{SL}(3,\mathbb Z)\) ⋮ Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture ⋮ Homotopy-theoretic E-theory and \(n\)-order ⋮ Model theoretic reformulation of the Baum-Connes and Farrell-Jones conjectures ⋮ Field theory configuration spaces for connective ko-theory ⋮ A non-commutative model for higher twistedK-theory ⋮ Unit spectra of \(K\)-theory from strongly self-absorbing \(C^\ast\)-algebras ⋮ Homotopy theory with *categories ⋮ Algebraic \(K\)-theory, \(K\)-regularity, and \(\mathbb T\)-duality of \(\mathcal O_\infty\)-stable \(C^\ast\)-algebras

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