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Groups acting freely on R-trees

Published online by Cambridge University Press:  19 September 2008

John W. Morgan  and
Richard K. Skora
John W. Morgan
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA
Richard K. Skora
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA
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Abstract

In this paper we study the question of which groups act freely on R-trees. The paper has two parts. The first part concerns groups which contain a non-cyclic, abelian subgroup. The following is the main result in this case.

Let the finitely presented group G act freely on an R-tree. If A is a non-cyclic, abelian subgroup of G, then A is contained in an abelian subgroup A′ which is a free factor of G.

The second part of the paper concerns groups whch split as an HNN-extension along an infinite cyclic group. Here is one formulation of our main result in that case.

Let the finitely presented group G act freely on an R-tree. If G has an HNN-decomposition

where (s) is infinite cyclic, then there is a subgroup H′ ⊂ H such that either

(a) ; or

(b) , where S is a closed surface of non-positive Euler characteristic.

A slightly different, more precise result is also given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 737 - 756
Copyright
Copyright © Cambridge University Press 1991

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References

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