Definition and characterization of continuous bounded cohomology
One of the important features of the theory of continuous bounded cohomology is that the bi-functors H•cb come with a natural transformation Ψ • : H•cb → H• c to the continuous cohomology H• c or to the Eilenberg-MacLane cohomology if the group under consideration is discrete. As a matter of fact, most applications of bounded continuous cohomology are intimately connected with the properties of these comparison maps :
On one hand, the kernel of Ψ2 has very concrete interpretations in terms of quasimorphisms and more generally of rough actions, as we shall see in Section 13.3.
KeywordsNormal Subgroup Topological Group Compact Group Short Exact Sequence Countable Group
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