#### 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

Email: mjd@maths.soton.ac.uk

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