The Baum--Connes conjecture localised at the unit element of a discrete\n group

2018/07/16 by Paolo Antonini, Antonini, Paolo, Sara Azzali +3 · 1 citation
Mathematics · #19D55 (Secondary) #19K35 #46L80 (Primary) #55R40 #58J22 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1807.05892

openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a Baum--Connes assembly map localised at the unit element of a\ndiscrete group \Γ. This morphism, called \μ_\τ, is defined in\nKK-theory with coefficients in \ℝ by means of the action of the\nprojection [\τ]\∈ KK_\ℝ^\Γ(\ℂ,\ℂ)\ncanonically associated to the group trace of \Γ. We show that the\ncorresponding \τ-Baum--Connes conjecture is weaker then the classical one\nbut still implies the strong Novikov conjecture. The right hand side of\n\μ_\τ is functorial with respect to the group \Γ.\n

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