We give an account of convergence groups from the point of view of groups which act properly discontinuously on spaces of distinct triples. We give a proof of the equivalence of this characterisation with the dynamical definition of Gehring and Martin. We focus our attention on uniform convergence groups, i.e. those for which the action on the space of distinct triples is also cocompact, and explore some of their properties from a purely dynamical point of view. We show that the space of distinct unordered $ n $-tuples in any continuum is connected. Moreover, the spaces of distinct ordered $ n $-tuples in any metrisable continuum other than a circle or an arc is also connected.
in : Geometric Group Theory Down Under, Proceedings of a Special Year in Geometric Group Theory, Canberra, Australia (ed. J.Cossey, C.F.Miller III, W.D.Neumann, M.Shapiro), de Gruyter (1999) 23-54.