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Bounded Cohomology, a Rough Outline

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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

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