We show that the isomorphism induced by the inclusion of pairs \$(X,\emptyset)\subset (X,Y)\$ between the relative bounded cohomology of \$(X,Y)\$ and the bounded cohomology of \$X\$ is isometric in degree at least 2 if the fundamental group of each connected component of \$Y\$ is amenable. As an application we provide a self-contained proof of Gromov Equivalence theorem and a generalization of a result of Fujiwara and Manning on the simplicial volume of generalized Dehn fillings.

### Isometric properties of relative bounded cohomology

#### Abstract

We show that the isomorphism induced by the inclusion of pairs \$(X,\emptyset)\subset (X,Y)\$ between the relative bounded cohomology of \$(X,Y)\$ and the bounded cohomology of \$X\$ is isometric in degree at least 2 if the fundamental group of each connected component of \$Y\$ is amenable. As an application we provide a self-contained proof of Gromov Equivalence theorem and a generalization of a result of Fujiwara and Manning on the simplicial volume of generalized Dehn fillings.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11568/158485`
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