Trees树
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作者： Jean-Pierre Serre等著
出 版 社： 湖南文艺出版社
出版时间： 2003-2-1字数：版次： 1页数： 142印刷时间： 2003/02/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540442370包装： 精装内容简介
"Serre's notes on groups acting on trees have appeared in various forms (all in French) over the past ten years and they have had a profound influence on the development of many areas, for example, the theory of ends of discrete groups. This fine translation is very welcome and I strongly recommend it as an introduction to an important subject. In Chapter I, which is self-contained, the pace is fairly gentle. The author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the (rather difficult) proof of the general case." (A.W. Mason in Proceedings of the Edinburgh Mathematical Society 1982)
目录
Introduction
Chapterapter. I Trees and Amalgams
1 Amalgams
1.1 Direct limits
1.2 Structure of amalgams
1.3 Consequences of the structure theorem
1.4 Constructions using amalgams
1.5 Examples
2 Trees
2.1 Graphs
2.2 Trees
2.3 Subtrees of a graph
3 Trees and free groups
3.1 Trees of representatives
3.2 Graph of a free group
3.3 Free actions on a tree
3.4 Application: SChapterapterreier's theorem
Appedix:Presentation of a group of homeomorphisms
4 Trees and amalgams
4.1 The case of two factors
4.2 Examples of trees associated with amalgams
4.3 Applications
4.4 Limit of a tree of groups
4.5 Amalgams and fundamental domains (general case)
5 Structure of a group acting on a tree
5.1 Fundamental group of a graph of groups
5.2 Reduced words
5.3 Universal covering relative to a graph of groups
5.4 Structure theorem
5.5 Application: Kurosh's theorem
6 Amalgams and fixed points
6.1 The fixed point property for groups acting on trees
6.2 Consequences of property (FA)
6.3 Examples
6.4 Fixed points of an automorphism of a tree
6.5 Groups with fixed points (auxiliary results)
6.6 The case of SL[subscript 3](Z)
Chapter. II SL[subscript 2]
1 The tree of SL[subscript 2] over a local field
1.1 The tree
1.2 The groups GL(V) and SL(V)
1.3 Action of GL(V) on the tree of V; stabilizers
1.4 Amalgams
1.5 Ihara's theorem
1.6 Nagao's theorem
1.7 Connection with Tits systems
2 Arithmetic subgroups of the groups GL[subscript 2] and SL[subscript 2] over a function field of one variable
2.1 Interpretation of the vertices of [Gamma]\X as classes of vector bundles of rank 2 over C
2.2 Bundles of rank 1 and decomposable bundles
2.3 Structure of [Gamma]\X
2.4 Examples
2.5 Structure of [Gamma]
2.6 Auxiliary results
2.7 Structure of [Gamma]: case of a finite field
2.8 Homology
2.9 Euler-Poincare Chapteraracteristic
Bibliography
Index
