Isometric embeddings in bounded cohomology
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 grou...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 February 2014
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| In: |
Journal of topology and analysis
Year: 2014, Volume: 06, Issue: 01, Pages: 1-25 |
| ISSN: | 1793-7167 |
| DOI: | 10.1142/S1793525314500058 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1142/S1793525314500058 Verlag, Volltext: http://www.worldscientific.com/doi/abs/10.1142/S1793525314500058 
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| Author Notes: | M. Bucher, M. Burger, R. Frigerio, A. Iozzi, C. Pagliantini, M.B. Pozzetti |
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| 520 | |a 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. | ||
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