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Folding sequences

Folding sequences
Folding sequences
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.
groups acting on trees, free groups
139-158
Geometry & Topology Publications
Dunwoody, M.J.
ab9cba4b-1c90-4353-ad26-2b497d25cce3
Rivin, Igor
Rourke, Colin
Series, Caroline
Dunwoody, M.J.
ab9cba4b-1c90-4353-ad26-2b497d25cce3
Rivin, Igor
Rourke, Colin
Series, Caroline

Dunwoody, M.J. (1998) Folding sequences. In, Rivin, Igor, Rourke, Colin and Series, Caroline (eds.) The Epstein Birthday Schrift. (Geometry & Topology Monographs, 1) Coventry, UK. Geometry & Topology Publications, pp. 139-158.

Record type: Book Section

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.

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More information

Published date: 1998
Additional Information: ISSN 1464-8989
Keywords: groups acting on trees, free groups

Identifiers

Local EPrints ID: 29897
URI: http://eprints.soton.ac.uk/id/eprint/29897
PURE UUID: 3f3a1dcd-f026-4d9d-93b4-2b4be91a0bf0

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Date deposited: 15 May 2007
Last modified: 11 Dec 2021 15:16

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Contributors

Author: M.J. Dunwoody
Editor: Igor Rivin
Editor: Colin Rourke
Editor: Caroline Series

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