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].

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 |