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Properly discontinuous actions on Λ-trees

Published online by Cambridge University Press:  20 January 2009

I. M. Chiswell
I. M. Chiswell
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS
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Abstract

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The main result is a theorem giving several possibilities for the action of a 2-generator group acting on a Λ-tree, generalising the result that, if the action is free then the group is either free or free abelian. This involves investigation of several cases in which the action is shown to be properly discontinuous. This leads to a generalisation of results of Culler and Morgan, characterising abelian, dihedral and irreducible actions on ℝ-trees, to arbitrary Λ-trees.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 3 , October 1994 , pp. 423 - 444
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

1.Alperin, R. C. and Bass, H., Length functions of group actions on Λ-trees, in Combinatorial group theory and topology (ed. Gersten, S. M. and Stallings, J. R.) Annals of Mathematics Studies 111. Princeton: University Press 1987, 265–378.Google Scholar
2.Chiswell, I. M., Non-trivial group actions on Λ-trees, Bull. London Math. Soc. 24 (1992), 277–280.CrossRefGoogle Scholar
3.Chiswell, I. M., Harrison's theorem for Λ-trees, Quart. J. Math. Oxford (2) 45 (1994), 1–12.Google Scholar
4.Culler, M. and Morgan, J., Group actions on ℝ-trees, Proc. London Math. Soc. (3)55 (1987), 571–604.Google Scholar
5.Steiner, M., Gluing data and group actions on Λ-trees (Ph.D. thesis, Columbia University, 1988).Google Scholar
6.Zaitseva, M. I., Uspekhi Mat. Nauk 8(53) (1953), 135–137.Google Scholar