Introduction To Lambda Trees
Seiten
2001
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-4386-9 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-4386-9 (ISBN)
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An introductory text on lambda-trees. It should be suitable for research students in algebra and topology, and covers: the construction of lambda-trees; the isometries of lambda-trees; aspects of group actions on lambda-trees; free actions; and Rips' Theorem.
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.
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.
Lambda-trees and their construction; isometries of Lambda-trees; aspects of group actions on Lambda-trees; free actions; Rips' theorem.
| Erscheint lt. Verlag | 1.3.2001 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 981-02-4386-3 / 9810243863 |
| ISBN-13 | 978-981-02-4386-9 / 9789810243869 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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