4 papers
math.OA2026
The Baum-Connes and the Mishchenko-Kasparov assembly maps for group extensions
Jianguo Zhang
In this paper, we investigate the injectivity, surjectivity and isomorphism of the Baum--Connes assembly map with coefficients, and the injectivity of the Mishchenko--Ka…
math.OA2025
A localization algebra approach to the Baum-Connes conjecture for extensions
Jianguo Zhang
For an extension of discrete countable groups, it is known that the Baum-Connes conjecture with coefficients hold…
math.OA2025
The coarse Baum-Connes conjecture with filtered coefficients and product metric spaces
Jianguo Zhang
Inspired by the quantitative -theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There a…
math.OA2024
On the quantitative coarse Baum-Connes conjecture with coefficients
Jianguo Zhang
In this paper, we introduce the quantitative coarse Baum-Connes conjecture with coefficients (or QCBC, for short) for proper metric spaces which refines the coarse Baum-Connes conj…