Introduction to [lambda]-trees [[electronic resource] /] / Ian Chiswell

• Autore: Chiswell Ian <1948->
• Pubblicazione: Singapore ; ; River Edge, N.J., : World Scientific, c2001
• Descrizione fisica: 1 online resource (327 p.)
• Disciplina: 512.2
• Soggetto topico: Lambda algebra; Trees (Graph theory); Group theory
• Soggetto genere / forma: Electronic books.
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [297]-305) and index.
• Nota di contenuto: Contents ; Chapter 1. Preliminaries ; 1. Ordered abelian groups ; 2. Metric spaces ; 3. Graphs and simplicial trees ; 4. Valuations ; Chapter 2. Λ-trees and their Construction; 1. Definition and elementary properties ; 2. Special properties of R-trees; 3. Linear subtrees and ends ; 4. Lyndon length functions ; Chapter 3. Isometries of Λ-trees1. Theory of a single isometry ; 2. Group actions as isometries ; 3. Pairs of isometries ; 4. Minimal actions ; Chapter 4. Aspects of Group Actions on Λ-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 ; Chapter 5. Free Actions ; 1. Introduction ; 2. Harrison's Theorem ; 3. Some examples ; 4. Free actions of surface groups ; 5. Non-standard free groups ; Chapter 6. Rips' Theorem ; 1. Systems of isometries ; 2. Minimal components 3. Independent generators ; 4. Interval exchanges and conclusion ; References ; Index of Notation ; Index
• Sommario/riassunto: The theory of Λ-trees has its origin in the work of Lyndon on length functions in groups. The first definition of an <i>R</i>-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 <i>R</i>-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 <i>R</i>-trees, notably Rips' theorem on free actions. There
• Titolo autorizzato: Introduction to -trees
• ISBN: 1-281-95621-X; 9786611956219; 981-281-053-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910454383303321
• Lo trovi qui: Univ. Federico II