LAMBDA表达式树导论INTRODUCTION TO LAMBDA TREES

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.

Chapter 1. Preliminaries
1. Ordered abelian groups
2. Metric spaces
3. Graphs and simplicial trees
4. Valuations
Chapter 2. A-trees and their Construction
1. Definition and elementary properties
2. Special properties of R-trees
3. Linear subtrees and ends
4. Lyndon length functions
Chapter 3. Isometries of A-trees
1. Theory of a single isometry
2. Group actions as isometries
3. Pairs of isometries
4. Minimal actions
Chapter 4. Aspects of Group Actions on A-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
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
2. Minimal components
3. Independent generators
4. Interval exchanges and conclusion
References
Index of Notation
Index