Towards applications

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


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] :


Algebraic Group Compact Group Mapping Class Group Countable Group Finite Family 
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© Springer-Verlag Berlin Heidelberg 2001

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