Volume 1 (1998)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

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