The Baum--Connes conjecture localised at the unit element of a discrete group
Paolo Antonini, Sara Azzali, Georges Skandalis

TL;DR
This paper constructs a localized Baum--Connes assembly map at the unit element of a discrete group using KK-theory, showing it implies the strong Novikov conjecture and is weaker than the classical conjecture.
Contribution
It introduces a new localized assembly map in KK-theory at the group trace, providing a weaker but still impactful version of the Baum--Connes conjecture.
Findings
The localized assembly map $ au$-Baum--Connes conjecture implies the strong Novikov conjecture.
The map is functorial with respect to the group $ au$.
The conjecture is weaker than the classical Baum--Connes conjecture.
Abstract
We construct a Baum--Connes assembly map localised at the unit element of a discrete group . This morphism, called , is defined in -theory with coefficients in by means of the action of the projection canonically associated to the group trace of . We show that the corresponding -Baum--Connes conjecture is weaker then the classical one but still implies the strong Novikov conjecture. The right hand side of is functorial with respect to the group .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
