Volume 1 (1998)

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Folding sequences

M J Dunwoody

Geometry & Topology Monographs 1 (1998) 139–158
DOI: 10.2140/gtm.1998.1.139
 arXiv: math.GT/9810192
Abstract
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Bestvina and Feighn showed that a morphism $S\to T$ 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.

 Dedicated to David Epstein on the occasion of his 60th birthday.
Keywords
Groups acting on trees, free groups
Primary: 20E08
Secondary: 57M07