The Baum-Connes conjecture for extensions | Synapse
October 16, 2025Open Access
The Baum-Connes conjecture for extensions
Key Points
The counterexample shows that assumptions of the permanence property for the Baum-Connes conjecture cannot be simplified.
The permanence property previously proposed by Chabert and Echterhoff is challenged by this newly presented counterexample.
Understanding the limitations of the Baum-Connes conjecture is crucial for further developments in group theory.
This analysis underscores the importance of rigorous assumptions in mathematical conjectures related to group extensions.
Abstract
This note provides a counterexample showing that the assumptions that Chabert and Echterhoff have imposed in their permanence property of the Baum-Connes conjecture for group extensions cannot be simplified.