A localization algebra approach to the Baum-Connes conjecture for extensions

2025/06/23 by Zhang, Jianguo
#FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2506.18446

Abstract

For an extension 1→ N → Γ\xrightarrowq Γ/ N → 1 of discrete countable groups, it is known that the Baum-Connes conjecture with coefficients holds for Γ if it holds for Γ/ N and q^-1(F) for any finite subgroup F of Γ/ N. In this paper, we employ a localization algebra approach to prove this result.

Citations

• The Baum-Connes conjecture for extensions
• The coarse Baum-Connes conjecture with filtered coefficients and product metric spaces
• The Baum-Connes conjecture: an extended survey
• Dynamical complexity and controlled operator K-theory
• A categorical perspective on the Atiyah-Segal completion theorem in KK-theory

Related

• The Baum--Connes conjecture localised at the unit element of a discrete\n group
• The Baum-Connes conjecture for extensions
• A Complete Formulation of Baum-Conens' Conjecture for the Action of Discrete Quantum Groups
• Crossed product approach to equivariant localization algebras
• Local-global principle for the Baum-Connes conjecture with coefficients