Introduction to [lambda]-trees

Ian Chiswell9810243863, 9789810243869, 9789812810533

Introductory text for mathematicians and research students in algebra and topology, introducing the fundamental concepts and theory of A-Trees, including the origins and history of the theory. Discusses connections with other theories such as model theory and R-Trees.

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Table of contents :
Front cover……Page 1
Preface
……Page 4
Contents……Page 8
1. Ordered abelian groups……Page 10
2. Metric spaces……Page 15
3. Graphs and simplicial trees……Page 23
4. Valuations……Page 31
1. Definition and elementary properties……Page 38
2. Special properties of R-trees……Page 50
3. Linear subtrees and ends……Page 65
4. Lyndon length functions……Page 78
1. Theory of a single isometry……Page 88
2. Group actions as isometries……Page 97
3. Pairs of isometries……Page 107
4. Minimal actions……Page 124
1. Introduction……Page 136
2. Actions of special classes of groups……Page 139
3. The action of the special linear group……Page 153
4. Measured laminations……Page 159
5. Hyperbolic surfaces……Page 182
6. Spaces of actions on R-trees……Page 212
1. Introduction……Page 224
2. Harrison’s Theorem……Page 228
3. Some examples……Page 238
4. Free actions of surface groups……Page 242
5. Non-standard free groups……Page 246
1. Systems of isometries……Page 260
2. Minimal components……Page 274
3. Independent generators……Page 287
4. Interval exchanges and conclusion……Page 299
References……Page 306
Index of Notation……Page 316
Index……Page 318
Back cover……Page 325