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Towards applications

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

Abstract

The aim of this chapter is, firstly, to show what kind of applications pertinent to various fields can be derived from the theory of continuous bounded cohomology, and secondly to establish such results for concrete groups.

All this is concerned merely with bounded cohomology in degree two, for various coefficients. An example of very concrete computations in degree three based heavily on the cohomological techniques is given for SL33(R) and more general SLn by M. Burger and the author in [38], [113].

Moreover, an example of the benefit that one can derive from the metric information encapsulated in the whole theory, as emphasized in the head of Section 4, is the following result that we quote from [38] :

Keywords

  • Algebraic Group
  • Compact Group
  • Mapping Class Group
  • Countable Group
  • Finite Family

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). Towards applications. 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_6

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  • DOI: https://doi.org/10.1007/3-540-44962-0_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42054-5

  • Online ISBN: 978-3-540-44962-1

  • eBook Packages: Springer Book Archive