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" Trees "
transl. from the French by John Stillwell.
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BL
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| Record Number
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789722
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b609746
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| Main Entry
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transl. from the French by John Stillwell.
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| Title & Author
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Trees\ transl. from the French by John Stillwell.
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| Publication Statement
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Berlin [West]: Springer, 1980
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| Page. NO
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IX, 142 Seiten
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| ISBN
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0387101039
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: 3540101039
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: 9780387101033
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: 9783540101031
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| Notes
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Literaturverz. S. 137-139.
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| Contents
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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.- Appendix: 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 SL3(Z).- II. SL2.- 1 The tree of SL2 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 GL2 and SL2 over a function field of one variable.- 2.1 Interpretation of the vertices of F\X as classes of vector bundles of rank over C 96.- 2.2 Bundles of rank and decomposable bundles 99.- 2.3 Structure of ?\X.- 2.4 Examples.- 2.5 Structure of ?.- 2.6 Auxiliary results.- 2.7 Structure of ?: case of a finite field.- 2.8 Homology.- 2.9 Euler-Poincare characteristic.
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| Subject
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;Baum lt;Math.gt;
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| Subject
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Amalgam lt;Math.gt
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Lineare Gruppe.
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| LC Classification
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QA171.T736 1980
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| Added Entry
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Jean Pierre Serre
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John Stillwell
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| Parallel Title
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Arbres, Amalgames, SL2.
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