Sara Azzali
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View article: K-homology and K-theory of pure Braid groups
K-homology and K-theory of pure Braid groups Open
We produce an explicit description of the K-theory and K-homology of the pure braid group on $n$ strands. We describe the Baum--Connes correspondence between the generators of the left- and right-hand sides for $n=4$. Using functoriality o…
View article: The Baum-Connes conjecture localised at the unit element of a discrete group
The Baum-Connes conjecture localised at the unit element of a discrete group Open
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 idempotent canonically associated to the group trace…
View article: The Baum–Connes conjecture localised at the unit element of a discrete group
The Baum–Connes conjecture localised at the unit element of a discrete group Open
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 idempotent…
View article: Spectral 𝜁-invariants lifted to coverings
Spectral 𝜁-invariants lifted to coverings Open
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local fe…
View article: Two-cocycle twists and Atiyah–Patodi–Singer index theory
Two-cocycle twists and Atiyah–Patodi–Singer index theory Open
We construct η- and ρ-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…
View article: The Baum--Connes conjecture localised at the unit element of a discrete\n group
The Baum--Connes conjecture localised at the unit element of a discrete\n group Open
We construct a Baum--Connes assembly map localised at the unit element of a\ndiscrete group $\\Gamma$. This morphism, called $\\mu_\\tau$, is defined in\n$KK$-theory with coefficients in $\\mathbb{R}$ by means of the action of the\nproject…
View article: Lifted trace defect formulae on coverings
Lifted trace defect formulae on coverings Open
The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are shown to be preserved under lifting to the universal covering as a result of their local feature. In contrast, regularised trac…