Pozzetti, Maria B.
- Working Paper
This paper is devoted to the construction of norm-preserving maps between bounded cohomology groups. For a graph of groups with amenable edge groups we construct an isometric embedding of the direct sum of the bounded cohomology of the vertex groups in the bounded cohomology of the fundamental group of the graph of groups. With a similar technique we prove that if (X,Y) is a pair of CW-complexes and the fundamental group of each connected component of Y is amenable, the isomorphism between the relative bounded cohomology of (X,Y) and the bounded cohomology of X in degree at least 2 is isometric. As an application we provide easy and self-contained proofs of Gromov Equivalence Theorem and of the additivity of the simplicial volume with respect to gluings along \pi_1-injective boundary components with amenable fundamental group. Mehr anzeigen
Zeitschrift / SeriearXiv
Seiten / Artikelnummer
Organisationseinheit08802 - Iozzi, Alessandra (Tit.-Prof.)
03491 - Burger, Marc / Burger, Marc
AnmerkungenSubmitted on 12 May 2013. The text overlaps with the submission http://arxiv.org/abs/1205.1022 by the same authors. See also http://e-citations.ethbib.ethz.ch/view/pub:139342.