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Bounded Cohomology, a Rough Outline

  • Riccardo Benedetti
  • Carlo Petronio
Part of the Universitext book series (UTX)

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.

Keywords

Conjugacy Class Fundamental Group Fiber Bundle Amenable Group Polynomial Growth 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Riccardo Benedetti
    • 1
  • Carlo Petronio
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly

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