Overview

The theory of Lambda-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 Lambda-trees was established by Morgan and Shalen, who showed how to compactify a generalization of Teichmuller space for a finitely generated group using ""R""-trees. In that work they were led to define the idea of a Lambda-tree, where Lambda is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on ""R""-trees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups Lambda, including some interesting connections with model theory. ""Introduction to Lambda-Trees"" should prove useful for mathematicians and research students in algebra and topology.

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