The Baum–Connes conjecture localised at the unit element of a discrete group

DOI10.1112/S0010437X20007502zbMath1468.19007arXiv1807.05892OpenAlexW3119146474WikidataQ123144993 ScholiaQ123144993MaRDI QIDQ5150222

Sara Azzali, Paolo Antonini, Georges Skandalis

Publication date: 10 February 2021

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05892

zbMATH Keywords

classifying spacesNovikov conjectureassembly mapsequivariant Kasparov theory

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) (K)-theory and homology; cyclic homology and cohomology (19D55) Exotic index theories on manifolds (58J22) Kasparov theory ((KK)-theory) (19K35) Homology of classifying spaces and characteristic classes in algebraic topology (55R40)

Related Items (5)

Index theory on the Miščenko bundle ⋮ A note on twisted crossed products and spectral triples ⋮ \(K\)-theory of relative group \(C^*\)-algebras and the relative Novikov conjecture ⋮ The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces ⋮ Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras

Cites Work

• Unnamed Item
• Unnamed Item
• The Baum-Connes conjecture with coefficients for hyperbolic groups
• Expanders, exact crossed products, and the Baum-Connes conjecture
• Bivariant \(K\)-theory with \(\mathbb{R}/\mathbb{Z}\)-coefficients and rho classes of unitary representations
• The cyclic homology of the group rings
• Equivariant KK-theory and the Novikov conjecture
• Une notion de nucléarité en K-théorie (d'après J. Cuntz). (A notion of nuclearity in K-theory (in the sense of J. Cuntz))
• Random walk in random groups.
• Geometric \(K\)-theory for Lie groups and foliations
• Counterexamples to the Baum-Connes conjecture
• The minimal exact crossed product
• Half-exactness of the Kasparov equivariant bifunctor for amenable actions
• Flat bundles, von Neumann algebras andK-theory with ℝ/ℤ-coefficients
• The Baum–Connes conjecture: an extended survey
• Exact Sequences for the Kasparov Groups of Graded Algebras
• THE INDEX OF ELLIPTIC OPERATORS OVERC*-ALGEBRAS
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• K-theoretic amenability for discrete groups.
• On the geometry of burnside quotients of torsion free hyperbolic groups

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