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 di erent 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 in nite folding sequences are considered. One application is that a nitely generated inaccessible group must contain an in nite torsion subgroup. AMS Classi cation 20E08; 57M07