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Definition and characterization of continuous bounded cohomology

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1758)

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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