Francesco Milizia

activity

20242026

collaborators

6 papers

math.GT2026

On the cup product of De Rham classes in bounded cohomology

Roberto Frigerio, Francesco Milizia

On a negatively curved closed manifold, there exists a well-defined map $I^¨^{∙}$ associating to every closed differential form a bounded cohomology class via integration over s…

math.GR2025

Cohomological characterisation of hyperbolicity

Francesco Milizia, Nansen Petrosyan, Alessandro Sisto +1

For any geodesic metric space $X$ , we give a complete cohomological characterisation of the hyperbolicity of $X$ in terms of vanishing of its second $ℓ^{\infty}$ -cohomology. We…

math.GT2025

Minimal volume entropy of mapping tori over 3-manifolds

Giuseppe Bargagnati, Alberto Casali, Francesco Milizia +1

We prove that the minimal volume entropy of mapping tori over oriented closed smooth $3$ -manifolds vanishes. Our approach uses a variation of the amenable category and a suitable v…

math.GT2024

The action of mapping class groups on de Rham quasimorphisms

Giuseppe Bargagnati, Federica Bertolotti, Pietro Capovilla +1

We study the action of the mapping class group on the subspace of de Rham classes in the degree-two bounded cohomology of a hyperbolic surface. In particular, we show that the only…

math.GT2024

Simplicial maps between spheres and Davis' manifolds with positive simplicial volume

Francesco Milizia

We study the simplicial volume of manifolds obtained from Davis' reflection group trick, the goal being characterizing those having positive simplicial volume. In particular, we fo…

math.GR2024

Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov

Dario Ascari, Francesco Milizia

We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov…