Members & Guests

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 $\Gamma$.  The right hand side of $\mu_\tau$ is functorial with respect to the group $\Gamma$.

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):
4Secondary invariants for foliations

We construct $\eta$- and $\rho$-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah–Patodi–Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.

 

JournalMath. Proc. Camb. Philos. Soc.
PublisherCambridge University Press
VolumeAugust 2018
Link to preprint version
Link to published version

Related project(s):
4Secondary invariants for foliations

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