Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 7, pages 139-158.

Folding sequences

M J Dunwoody

Abstract. Bestvina and Feighn showed that a morphism S --> T between two simplicial trees that commutes with the action of a group G can be written as a product of elementary folding operations. Here a more general morphism between simplicial trees is considered, which allow different groups to act on S and T. It is shown that these morphisms can again be written as a product of elementary operations: the Bestvina-Feighn folds plus the so-called `vertex morphisms'. Applications of this theory are presented. Limits of infinite folding sequences are considered. One application is that a finitely generated inaccessible group must contain an infinite torsion subgroup.

Keywords. Groups acting on trees, free groups

AMS subject classification. Primary: 20E08. Secondary: 57M07.

E-print: arXiv:math.GT/9810192

Submitted: 27 October 1997. Published: 26 October 1998.

Notes on file formats

M J Dunwoody
Faculty of Math.Studies
University of Southampton
Southampton, SO9 5NH, UK

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