Isometric embeddings in bounded cohomology
- Bucher, M. Section de Mathématiques, Université de Genève, 2–4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland
- Burger, M. Department Mathematik, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
- Frigerio, R. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
- Iozzi, A. Department Mathematik, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
- Pagliantini, C. Fakultät für Mathematik Universität Regensburg, Universitätsstrasse 31 93053 Regensburg, Germany
- Pozzetti, M. B. Department Mathematik, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
- 2014-2-13
Published in:
- Journal of Topology and Analysis. - World Scientific Pub Co Pte Lt. - 2014, vol. 06, no. 01, p. 1-25
English
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's Equivalence Theorem and of the additivity of the simplicial volume with respect to gluings along π1 -injective boundary components with amenable fundamental group.
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1142/s1793525314500058
- ISSN 1793-5253
- Persistent URL
- https://sonar.ch/global/documents/275327
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