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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


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.

Dedicated to David Epstein on the occasion of his 60th birthday.


Groups acting on trees, free groups

Mathematical Subject Classification

Primary: 20E08

Secondary: 57M07


Received: 27 October 1997
Published: 22 October 1998

M J Dunwoody
Faculty of Mathematical Studies
University of Southampton
United Kingdom