Archimedean actions on median pretrees

Bowditch, Brian H. and Crisp, John (2001) Archimedean actions on median pretrees. Mathematical Proceedings of the Cambridge Philosophical Society, 130 (3), 383-400. (doi:10.1017/S0305004101004996).

Abstract

In this paper we consider group actions on generalized treelike structures (termed ‘pretrees’) defined simply in terms of betweenness relations. Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an [open face R]-tree. Thus the theory of isometric actions on [open face R]-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups. This approach has application also to the study of convergence group actions on continua.

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