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Introduction to Lambda Trees

Introduction to Lambda Trees by Ian Chiswell
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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 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 Λ, including some interesting connections with model theory.

Introduction to Λ-Trees will prove to be useful for mathematicians and research students in algebra and topology.

  • Λ-Trees and Their Construction
  • Isometries of Λ-Trees
  • Aspects of Group Actions on Λ-Trees
  • Free Actions
  • Rips' Theorem

Readership: Mathematicians and research students in algebra and topology.
World Scientific Publishing Company; February 2001
328 pages; ISBN 9789814492584
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Title: Introduction to Lambda Trees
Author: Ian Chiswell
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