1.

Record Nr.

UNINA9910454383303321

Autore

Chiswell Ian <1948->

Titolo

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

Pubbl/distr/stampa

Singapore ; ; River Edge, N.J., : World Scientific, c2001

ISBN

1-281-95621-X

9786611956219

981-281-053-6

Descrizione fisica

1 online resource (327 p.)

Disciplina

512.2

Soggetti

Lambda algebra

Trees (Graph theory)

Group theory

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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