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Author Chiswell, Ian, 1948-
Title Introduction to [lambda]-trees / Ian Chiswell.
Imprint Singapore ; River Edge, N.J. : World Scientific, ©2001.

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 297-305) 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 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.
Summary "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 space for a finitely generated group using R-trees. 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 R-trees, 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.)
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

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