TY  - BOOK
AU  - Serre,Jean-Pierre
TI  - Trees
T2  - Springer monographs in mathematics,
SN  - 3540442375
AV  - QA166.2 .S37 1980
PY  - 1980///
CY  - Berlin, New York
PB  - Springer
KW  - Trees (Graph theory)
KW  - Linear algebraic groups
KW  - Free groups
N1  - Includes bibliographical references (pages [137]-139) and index; Contents; Introduction; Ch. 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: Schreier's theorem; App. 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); Ch. 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 characteristic; Bibliography; Index
ER  -