Introduction to Lambda Trees
By: Ian Chiswell (author)Hardback
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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 generalisation 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 will prove to be useful for mathematicians and research students in algebra and topology.
Lambda-trees and their construction; isometries of Lambda-trees; aspects of group actions on Lambda-trees; free actions; Rips' theorem.
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- ID: 9789810243869
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