Isometric properties of relative bounded cohomology

Abstract

We show that the isomorphism induced by the inclusion of pairs $(X,\varnothing )\subset (X,Y)$ 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.

arXiv commentThere is one more author, as well as three more theorems

References in corpus (1)

• Relative measure homology and continuous bounded cohomology of topological pairs

Cited by in corpus (5)

• The simplicial volume of 3-manifolds with boundary
• Stable integral simplicial volume of 3-manifolds
• Simplicial volume of compact manifolds with amenable boundary
• Proportionality principle for the simplicial volume of families of Q-rank 1 locally symmetric spaces
• On the equivalence of the definitions of volume of representations