Author 
Chiswell, Ian, 1948

Subject 
Lambda algebra.


Trees (Graph theory)


Group theory.

Description 
1 online resource (x, 315 pages) : illustrations 
Bibliography Note 
Includes bibliographical references (pages 297305) and index. 
Note 
Print version record. 
Contents 
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 Rtrees. 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 Rtrees  ch. 5. Free actions. 1. Introduction. 2. Harrison's theorem. 3. Some examples. 4. Free actions of surface groups. 5. Nonstandard free groups  ch. 6. Rips' theorem. 1. Systems of isometries. 2. Minimal components. 3. Independent generators. 4. Interval exchanges and conclusion. 
Summary 
"The theory of [lambda]trees has its origin in the work of Lyndon on length functions in groups. The first definition of an Rtree 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 space for a finitely generated group using Rtrees. In that work they were led to define the idea of a [lambda]tree, where [lambda] is an arbitrary ordered abelian group. Since then there has been much progress in understanding the structure of groups acting on Rtrees, notably Rips' theorem on free actions. There has also been some progress for certain other ordered abelian groups [lambda], including some interesting connections with model theory. Introduction to [lambda]Trees will prove to be useful for mathematicians and research students in algebra and topology." 
ISBN 
9789812810533 (electronic bk.) 

9812810536 (electronic bk.) 

128195621X 

9781281956217 

9789810243869 

9810243863 
OCLC # 
268962256 
Additional Format 
Print version: Chiswell, Ian, 1948 Introduction to [lambda]trees. Singapore ; River Edge, N.J. : World Scientific, ©2001 9810243863 9789810243869 (DLC) 2001281032 (OCoLC)47032651 
