04220nam 2200625Ia 450 991078238910332120230607222148.01-281-95621-X9786611956219981-281-053-6(CKB)1000000000538090(EBL)1681612(OCoLC)879025483(SSID)ssj0000182337(PQKBManifestationID)11178506(PQKBTitleCode)TC0000182337(PQKBWorkID)10166843(PQKB)10836138(MiAaPQ)EBC1681612(WSP)00004495(Au-PeEL)EBL1681612(CaPaEBR)ebr10255889(EXLCZ)99100000000053809020010530d2001 uy 0engur|n|---|||||txtccrIntroduction to [lambda]-trees[electronic resource] /Ian ChiswellSingapore ;River Edge, N.J. World Scientificc20011 online resource (327 p.)Description based upon print version of record.981-02-4386-3 Includes bibliographical references (p. [297]-305) and index.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 functionsChapter 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 laminations5. 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 isometries2. Minimal components 3. Independent generators ; 4. Interval exchanges and conclusion ; References ; Index of Notation ; Index 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. ThereLambda algebraTrees (Graph theory)Group theoryLambda algebra.Trees (Graph theory)Group theory.512.2Chiswell Ian1948-319946MiAaPQMiAaPQMiAaPQBOOK9910782389103321Introduction to -trees3739442UNINA