Introduction To Lambda Trees

The theory of Λ-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an R-tree was given by Tits in 1977. The importance of Λ-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmüller space for a finitely generated group using R-trees. In that work they were led to define the idea of a Λ-tree, where Λ is an arbitrary ordered abelian group. Since then there has been much progress in understanding the struc