Abstract
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.
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© 1992 Springer-Verlag Berlin Heidelberg
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Benedetti, R., Petronio, C. (1992). Bounded Cohomology, a Rough Outline. In: Lectures on Hyperbolic Geometry. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58158-8_6
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DOI: https://doi.org/10.1007/978-3-642-58158-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55534-6
Online ISBN: 978-3-642-58158-8
eBook Packages: Springer Book Archive