Paolo Antonini
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View article: A proof of the Hamiltonian Thom Isotopy Lemma
A proof of the Hamiltonian Thom Isotopy Lemma Open
In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are Hamiltonian isotopic.
View article: Optimal transport between algebraic hypersurfaces
Optimal transport between algebraic hypersurfaces Open
What is the optimal way to deform a projective hypersurface into another one? In this paper we will answer this question adopting the point of view of measure theory, introducing the optimal transport problem between complex algebraic proj…
View article: A Note on Twisted Crossed Products and Spectral Triples
A Note on Twisted Crossed Products and Spectral Triples Open
Starting with a spectral triple on a unital $C^{*}$-algebra $A$ with an action of a discrete group $G$, if the action is uniformly bounded (in a Lipschitz sense) a spectral triple on the reduced crossed product $C^{*}$-algebra $A\rtimes_{r…
View article: Geometry of Grassmannians and optimal transport of quantum states
Geometry of Grassmannians and optimal transport of quantum states Open
Let $\mathsf{H}$ be a separable Hilbert space. We prove that the Grassmannian $\mathsf{P}_c(\mathsf{H})$ of the finite dimensional subspaces of $\mathsf{H}$ is an Alexandrov space of nonnegative curvature and we employ its metric geometry …
View article: Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras
Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras Open
We strengthen a result of Hanke-Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group C*-algebra holds for many other exotic group C*-algebras, in particular t…
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: Integrable lifts for transitive Lie algebroids
Integrable lifts for transitive Lie algebroids Open
Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive a…
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: The injectivity radius of Lie manifolds
The injectivity radius of Lie manifolds Open
We prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive