The Baum-Connes assembly map and the generalized Bass conjecture

2007/07/25 by Crichton Ogle, Ogle, C.
Mathematics · #46L80 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0707.3655

openalex publication_date 2007/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the image of Connes-Karoubi-Chern character, restricted to the image of the Baum-Connes assembly map in the Bott-periodized topological K-theory of the complex group algebra, lies in the elliptic summand of the (periodic) cyclic homology of the group algebra. This implies that for any (weighted) ell-1 completion of the group algebra, rational surjectivity of the Baum-Connes assembly map implies the generalized Bass conjecture for that algebra.

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