The Baum–Connes assembly map, delocalization and the Chern character
| Autor: | Michel Matthey |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Pure mathematics
Mathematics(all) Degree (graph theory) Discrete group General Mathematics Baum–Connes conjecture Assembly map State (functional analysis) K-theory K-homology Chern character Character (mathematics) Mathematics::K-Theory and Homology Domain (ring theory) Equivariant map Algebraic number Mathematics Group ring |
| Zdroj: | Advances in Mathematics. 183(2):316-379 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/s0001-8708(03)00090-2 |
| Popis: | For a discrete group Γ, we explicitly describe the rational Baum–Connes assembly map μ ∗ Γ ⊗id C in “homological degree ⩽2” and show that in this domain it factors through the algebraic K-theory of the complex group ring of Γ. We also state and prove a delocalization property for μ ∗ Γ , namely expressing it rationally in terms of the Novikov assembly map. Finally, we give a handicrafted construction of the delocalized equivariant Chern character (in the analytic language) and prove that it coincides with the equivariant Chern character of Luck (Invent. Math. 149 (2002) 123–152) (defined in the topological framework). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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