Abstract
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.
Keywords
- Normal Subgroup
- Topological Group
- Compact Group
- Short Exact Sequence
- Countable Group
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Definition and characterization of continuous bounded cohomology. In: Monod, N. (eds) Continuous Bounded Cohomology of Locally Compact Groups. Lecture Notes in Mathematics, vol 1758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44962-0_4
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DOI: https://doi.org/10.1007/3-540-44962-0_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42054-5
Online ISBN: 978-3-540-44962-1
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