## Dr. Sara Azzali

### Project leader

Universität Potsdam

E-mail: azzali(at)uni-potsdam.de

Telephone: +49 331 977-1629

Homepage: http://www.math.uni-potsdam.de/~azzali/

## Publications within SPP2026

We construct a Baum--Connes assembly map localised at the unit element of a discrete group $\Gamma$.

This morphism, called $\mu_\tau$, is defined in $KK$-theory with coefficients in $\mathbb{R}$ by means of the action of the projection $[\tau]\in KK_\mathbb{R}^\Gamma(\mathbb{C},\mathbb{C})$ canonically associated to the group trace of $\Gamma$.

We show that the corresponding $\tau$-Baum--Connes conjecture is weaker then the classical one but still implies the strong Novikov conjecture.

**Related project(s):****4**Secondary invariants for foliations