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Introduction to [lambda]-trees /
"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 Teichmüller spa...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, N.J. :
World Scientific,
©2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Ch. 1. Preliminaries. 1. Ordered abelian groups. 2. Metric spaces. 3. Graphs and simplicial trees. 4. Valuations
- ch. 2. [lambda]-trees and their construction. 1. Definition and elementary properties. 2. Special properties of R-trees. 3. Linear subtrees and ends. 4. Lyndon length functions
- ch. 3. Isometries of [lambda]-trees. 1. Theory of a single isometry. 2. Group actions as isometries. 3. Pairs of isometries. 4. Minimal actions
- ch. 4. Aspects of group actions on [lambda]-trees. 1. Introduction. 2. Actions of special classes of groups. 3. The action of the special linear group. 4. Measured laminations. 5. Hyperbolic surfaces. 6. Spaces of actions on R-trees
- ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Non-standard free groups
- ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion.