Introduction to [lambda]-trees / Ian Chiswell.

Format:

Book

Author/Creator:

Chiswell, Ian, 1948-

Language:

English

Subjects (All):

Lambda algebra.

Trees (Graph theory).

Group theory.

Physical Description:

1 online resource (327 p.)

Edition:

1st ed.

Place of Publication:

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

Language Note:

English

Summary:

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

Contents:

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [297]-305) and index.

ISBN:

9786611956219

9781281956217

128195621X

9789812810533

9812810536

OCLC:

879025483