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010   $a1-281-95621-X
010   $a9786611956219
010   $a981-281-053-6
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100   $a20010530d2001      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to [lambda]-trees$b[electronic resource] /$fIan Chiswell
210   $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$dc2001
215   $a1 online resource (327 p.)
300   $aDescription based upon print version of record.
311   $a981-02-4386-3 
320   $aIncludes bibliographical references (p. [297]-305) and index.
327   $aContents               ; Chapter 1. Preliminaries                               ; 1. Ordered abelian groups                                ; 2. Metric spaces                       ; 3. Graphs and simplicial trees                                     ; 4. Valuations                    ; Chapter 2. ?-trees and their Construction; 1. Definition and elementary properties                                              ; 2. Special properties of R-trees; 3. Linear subtrees and ends                                  ; 4. Lyndon length functions
327   $aChapter 3. Isometries of ?-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 ?-trees; 1. Introduction                      ; 2. Actions of special classes of groups                                              ; 3. The action of the special linear group                                                ; 4. Measured laminations
327   $a5. 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
327   $a2. Minimal components                            3. Independent generators                                ; 4. Interval exchanges and conclusion                                           ; References                 ; Index of Notation                        ; Index
330   $a The theory of ?-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 ?-trees was established by Morgan and Shalen, who showed how to compactify a generalisation of Teichmu?ller space for a finitely generated group using <i>R</i>-trees. In that work they were led to define the idea of a ?-tree, where ? 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
606   $aLambda algebra
606   $aTrees (Graph theory)
606   $aGroup theory
615  0$aLambda algebra.
615  0$aTrees (Graph theory)
615  0$aGroup theory.
676   $a512.2
700   $aChiswell$b Ian$f1948-$0319946
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910782389103321
996   $aIntroduction to -trees$93739442
997   $aUNINA