Bucher, M. and Burger, M. and Frigerio, R. and Iozzi, A. and Pagliantini, C. and Pozzetti, M. B. (2014) Isometric embeddings in bounded cohomology. JOURNAL OF TOPOLOGY AND ANALYSIS, 6 (1). pp. 1-25. ISSN 1793-5253, 1793-7167
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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 pi(1)-injective boundary components with amenable fundamental group.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SIMPLICIAL VOLUME; GROMOV INVARIANT; MANIFOLDS; 3-MANIFOLDS; MAPS; Relative bounded cohomology; isometries in bounded cohomology; simplicial volume; graph of groups; additivity of the simplicial volume; Dehn filling; l(1)-homology; Gromov Equivalence Theorem |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Nov 2019 10:50 |
| Last Modified: | 18 Nov 2019 10:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/10617 |
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