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EXOTIC ACTIONS ON TREES

Published online by Cambridge University Press:  01 May 1997

CHARLES HOLTON  and
LUCA Q. ZAMBONI
CHARLES HOLTON
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-3840, USA
LUCA Q. ZAMBONI
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116, USA
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Abstract

We give an explicit example of an exotic (non-simplicial), geometric free action of the free group [ ]3 on an ℝ-tree T. We begin by associating an interval translation mapping of the unit interval to an automorphism ψ of [ ]3. We use a result of D. Gaboriau and G. Levitt to obtain an [ ]3-action on an ℝ-tree T. We show that for our particular choice of ψ, the resulting [ ]3-action is minimal, free and exotic.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 309 - 313
Copyright
© The London Mathematical Society 1997

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