LAMBDA表达式树导论INTRODUCTION TO LAMBDA TREES
2001-12
Aspen Publishers
Chiswell, Ian
315
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. ValuationsChapter 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 functionsChapter 3. Isometries of A-trees 1. Theory of a single isometry 2. Group actions as isometries 3. Pairs of isometries 4. Minimal actionsChapter 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-treesChapter 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 conclusionReferencesIndex of NotationIndex
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