ℓ∞\ell^\infty-cohomology, bounded differential forms and isoperimetric inequalities

We revisit Gersten's $\ell^\infty$-cohomology of groups and spaces, removing the finiteness assumptions required by the original definition while retaining its geometric nature. Mirroring the corresponding results in bounded cohomology, we provide a characterization of amenable groups using $\ell^\infty$-cohomology, and generalize Mineyev's characterization of hyperbolic groups via $\ell^\infty$-cohomology to the relative setting. We describe how $\ell^\infty$-cohomology is related to isoperimetric inequalities. We prove an adaptation of the de Rham's theorem in the context of $\ell^\infty$-cohomology. Lastly, we consider some algorithmic problems concerning $\ell^\infty$-cohomology and show that they are undecidable.Comment: 38 pages. Added in v3: a characterization of relative hyperbolicity and some undecidability result

Bounded differential forms and coinvariants of bounded functions

Given a group $G$ acting cocompactly on a smooth manifold $M$ by deck transformations, there is an integration map, defined recently by Kato, Kishimoto and Tsutaya, from the top-degree bounded de Rham cohomology of $M$ to the coinvariants $\ell^\infty(G)_G$. We generalize its definition and show that it is an isomorphism. In the presence of boundary, a relative version of bounded de Rham cohomology is considered.Comment: 11 page

The action of mapping class groups on de Rham quasimorphisms

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 fixed nontrivial finite-dimensional subspace is the one generated by the Euler class. As a consequence, we get that the action of the mapping class group on the space of de Rham quasimorphisms has no fixed points.Comment: 21 pages, 4 figures. Comments are welcome

Coomologia a valori limitati

L'oggetto di studio di questa tesi è la coomologia a valori limitati, introdotta da Gersten nei primi anni 90. La coomologia a valori limitati di uno spazio X (tipicamente una varietà differenziabile o un CW-complesso) riesce a catturare alcuni aspetti della geometria su larga scala del rivestimento universale di X. Essa è legata, in particolare, a fenomeni tipici della curvatura negativa, come la validità di opportune disuguaglianze isoperimetriche. Nel contesto dei gruppi finitamente presentati, può essere utilizzata per caratterizzare i gruppi iperbolici. Nel contesto della geometria Riemanniana, è legata a una congettura di Gromov riguardante l'esistenza di primitive limitate di forme differenziali definite sul rivestimento universale di una varietà Riemanniana compatta. Cohomology with bounded values has been introduced by Gersten in the early 90s. The cohomology with bounded values of a space X (typically, a differentiable manifold or a CW-complex) is able to detect some aspects of the large scale geometry of the universal cover of X, especially those related to negative curvature phenomena, such as the presence of isoperimetric inequalities. In the setting of finitely generated groups, cohomology with bounded values can be used to give a characterization of hyperbolic groups. In the setting of Riemannian geometry, it has a close relationship with a conjecture by Gromov on the existence of bounded primitives for differentiable forms defined on the universal cover of a compact Riemannian manifold

Arte de saber ver en las bellas artes del diseño

En la p. [5] aparece, 182

Osservazioni ed aggiunte ai pincipii di architettura civile

di Francesco Milizia ; proposte agli studiosi ed amatori dell'architettura dal Prof. Giovanni Antolin

Principii di architettura civile

di Francesco MiliziaTomo 1: 280 S., 10 Taf. ; tomo 2: 308 S., 13 Taf. ; tomo 3: 263 S., 1 Tab., 13 Taf

Arte de ver en las bellas artes del diseño según los principios de Sulzer y de Mengs

Signaturizad

La storia dell'astronomia

di M. Bailly; ridotta in compendio dal Signor Francesco MiliziaAutor: Jean Sylvain Bailly (1736-1793