Bounded Cohomology, a Rough Outline
In this chapter we point out some of the basic ideas of the theory of bounded cohomology we first met during the proof of the rigidity theorem (Sect. C.3: compare F.2.2 below). In particular we define the groups of singular bounded cohomology and we consider the natural class of cohomology arising from the problem of the existence of a global non-vanishing section on a flat fiber bundle (known as Euler class of the bundle). In connection with the notion of Euler class we introduce and develop the definition of amenable group.
KeywordsConjugacy Class Fundamental Group Fiber Bundle Amenable Group Polynomial Growth
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