Amenability appears as one of the fundamental concepts bridging the worlds of functional analysis and geometric group theory. A group is said to be amenable if it admits an invariant mean on the space of bounded functions on the group.
There are several well known homological and cohomological characterisations of amenability including Johnson’s celebrated characterisation of amenability in terms of vanishing bounded cohomology, and an alternative homological view of amenability provided by Block and Weinberger who showed that for a metric space amenability could be characterised by non vanishing uniformly finite homology. In this project we showed that the there is a natural short exact sequence which naturally relates the two theories via dualisation.