scholarly journals Relative bounded cohomology for groupoids

2016 ◽  
Vol 184 (1) ◽  
pp. 27-66
Author(s):  
Matthias Blank
Keyword(s):  
Bounded Cohomology ◽  
Relative Bounded Cohomology

scholarly journals Isometric embeddings in bounded cohomology

2014 ◽  
Vol 06 (01) ◽  
pp. 1-25 ◽  
Author(s):  
M. Bucher ◽  
M. Burger ◽  
R. Frigerio ◽  
A. Iozzi ◽  
C. Pagliantini ◽  
...  
Keyword(s):  
Fundamental Group ◽  
Isometric Embedding ◽  
Equivalence Theorem ◽  
Connected Component ◽  
Bounded Cohomology ◽  
Graph Of Groups ◽  
Simplicial Volume ◽  
Direct Sum ◽  
Isometric Embeddings ◽  
Relative 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 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.

scholarly journals Barycentric straightening and bounded cohomology

2018 ◽  
Vol 21 (2) ◽  
pp. 381-403 ◽  
Author(s):  
Jean-François Lafont ◽  
Shi Wang
Keyword(s):  
Bounded Cohomology

scholarly journals The cup product of Brooks quasimorphisms

2018 ◽  
Vol 30 (5) ◽  
pp. 1157-1162 ◽  
Author(s):  
Michelle Bucher ◽  
Nicolas Monod
Keyword(s):  
Free Group ◽  
Automorphism Groups ◽  
Bounded Cohomology ◽  
Universal Class ◽  
Cup Product

AbstractWe prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups.

scholarly journals Bounded cohomology of amenable covers via classifying spaces

2020 ◽  
Vol 66 (1) ◽  
pp. 151-172
Author(s):  
Clara Löh ◽  
Roman Sauer
Keyword(s):  
Classifying Spaces ◽  
Bounded Cohomology

Bounded Cohomology, a Rough Outline

1992 ◽  
pp. 273-320
Author(s):  
Riccardo Benedetti ◽  
Carlo Petronio
Keyword(s):  
Bounded Cohomology ◽  
Rough Outline
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