TreesFrom the reviews: "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) |
Contents
| x | |
Chapter II | 11 |
2 Trees | 13 |
3 Trees and free groups | 25 |
1 The tree of SL2 over a local field | 28 |
4 Trees and amalgams | 32 |
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Common terms and phrases
acts freely acts without inversion algebra amalgam automorphism B₁ backtracking bijection Bourbaki bundle of rank canonical Card(S chap compact congruence subgroups conjugate connected contains Corollary corresponding cusp Deduce defined deg(F denote det(E direct limit disjoint union elements equivalent Euler-Poincaré characteristic exact sequence example exerc finite index fixed point free group fundamental domain fundamental group G acts G₁ G₂ geodesic geometric edge GL(V graph of groups group acting group G H₁ homomorphism hypothesis induces infinite injective integer isomorphic kernel L₁ lattice lemma Let G maximal tree mod G morphism non-empty normal subgroup P₁ P₁(K Pic(A proof prop Proposition quotient Remark resp S₁ Show stabilizer subbundle subgraph subgroup of finite subgroup of G subset subtree Suppose surjective T₁ theorem Tits system torsion-free tree of groups vector bundle vert vertex whence ye edge