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Archimedean actions on median pretrees

Published online by Cambridge University Press:  18 May 2001

BRIAN H. BOWDITCH  and
JOHN CRISP
BRIAN H. BOWDITCH
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ. e-mail: [email protected]
JOHN CRISP
Affiliation:
Laboratoire de Topologie, Université de Bourgogne, UMR 5584 du CNRS, B.P. 47 870, 21078 Dijon, France
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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 ℝ-tree. Thus the theory of isometric actions on 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 3 , May 2001 , pp. 383 - 400
Copyright
2001 Cambridge Philosophical Society

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