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Folding sequences. (English) Zbl 0927.20013

Rivin, Igor (ed.) et al., The Epstein Birthday Schrift dedicated to David Epstein on the occasion of his 60th birthday. Warwick: University of Warwick, Institute of Mathematics, Geom. Topol. Monogr. 1, 139-158 (1998).
Summary: 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.
For the entire collection see [Zbl 0901.00063].

MSC:

20E08 Groups acting on trees
57M07 Topological methods in group theory
20E07 Subgroup theorems; subgroup growth
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