Let X be a topological space, and let C(X) be the complex of singular cochains on X with real coefficients. We denote by Cc(X) the subcomplex given by continuous cochains, i.e. by such cochains whose restriction to the space of simplices (endowed with the compact-open topology) defines a continuous real function. We prove that at least for "reasonable" spaces the inclusion of Cc(X) in C(X) induces an isomorphism in cohomology, thus answering a question posed by Mostow. We also prove that such isomorphism is isometric with respect to the L^infty-norm on cohomology defined by Gromov. As an application, we discuss a cohomological proof of Gromov's proportionality principle for the simplicial volume of Riemannian manifolds.
|Autori interni:||FRIGERIO, ROBERTO|
|Titolo:||(Bounded) continuous cohomology and Gromov's proportionality principle|
|Anno del prodotto:||2011|
|Digital Object Identifier (DOI):||10.1007/s00229-010-0402-0|
|Appare nelle tipologie:||1.1 Articolo in rivista|