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Trees /
Serre, Jean-Pierre, 1926-
Trees / Jean-Pierre Serre ; translated from the French by John Stillwell - ix, 142 pages : illustrations ; 24 cm - Springer monographs in mathematics, 1439-7382 . - Springer monographs in mathematics, .
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.
3540442375
2003269778
Trees (Graph theory)
Linear algebraic groups
Free groups
QA166.2 / .S37 1980
Trees / Jean-Pierre Serre ; translated from the French by John Stillwell - ix, 142 pages : illustrations ; 24 cm - Springer monographs in mathematics, 1439-7382 . - Springer monographs in mathematics, .
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.
3540442375
2003269778
Trees (Graph theory)
Linear algebraic groups
Free groups
QA166.2 / .S37 1980
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