Trees/
Jean-Pierre Serre
- New York: Springer, 2003.
- ix, 142 p. : ill. ; 25 cm.
- (Springer monographs in mathematics) .
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.