Isometric properties of relative bounded cohomology

Michelle Bucher; Marc Burger; Roberto Frigerio; Alessandra Iozzi; Cristina Pagliantini; Maria Beatrice Pozzetti

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arXiv · 1205.1022

Isometric properties of relative bounded cohomology

Michelle Bucher·Marc Burger·Roberto Frigerio·Alessandra Iozzi·Cristina Pagliantini·Maria Beatrice Pozzetti

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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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BibTeX RIS

Michelle Bucher, Marc Burger, Roberto Frigerio, Alessandra Iozzi, Cristina Pagliantini, Maria Beatrice Pozzetti. 2012-05-18. Isometric properties of relative bounded cohomology. https://arxiv.org/abs/1205.1022

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