Mapping the homology of a group to the \(K\)-theory of its \(C^*\)-algebra
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Publication:1856568
zbMath1021.19003MaRDI QIDQ1856568
Publication date: 18 May 2003
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Chern characterreduced \(C^*\)-algebraintegral homologycountable discrete groupBaum-Connes's conjectureNovikov's strong conjecture
Connective (K)-theory, cobordism (19L41) (K)-theory and operator algebras (19K99) (K)-theory operations and generalized cohomology operations in algebraic topology (55S25) Riemann-Roch theorems, Chern characters (19L10)
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Quasi-representations of groups and two-homology ⋮ Geometric K-homology of flat D-branes ⋮ \(\mathrm C^*\)-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type ⋮ A counterexample to the HK-conjecture that is principal ⋮ The Baum-Connes assembly map, delocalization and the Chern character ⋮ Hecke operators in \(KK\)-theory and the \(K\)-homology of Bianchi groups ⋮ \(K\)-homology and \(K\)-theory of pure braid groups ⋮ Unbounded symmetric operators in \(K\)-homology and the Baum-Connes conjecture
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