## 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) |

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### Contents

II | 1 |

III | 2 |

IV | 5 |

V | 8 |

VI | 11 |

VII | 13 |

IX | 17 |

X | 21 |

XXX | 59 |

XXXI | 60 |

XXXII | 61 |

XXXIII | 64 |

XXXIV | 67 |

XXXV | 69 |

XXXVI | 74 |

XXXVII | 76 |

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### Common terms and phrases

acts freely acts without inversion algebraic amalgam automorphism backtracking bijection Bourbaki bundle of rank canonical Card(S chap compact congruence subgroups conjugate connected contains Corollary corresponding cusp Deduce defined deg(F denote denumerable det(E direct limit discrete subgroups disjoint union element of G equivalent Euler-Poincaré characteristic exact sequence example exerc finite index fixed point free group fundamental domain fundamental group G acts geodesic geometric edge GL(V graph of groups group acting group G homology homomorphism hypothesis induces infinite injective integer isomorphic kernel lattice lemma Let G Let H Math maximal tree mod G morphism non-empty normal subgroup notation Pevert Pic(A proof prop Proposition prove quotient reduced word Remark resp Show stabilizer subbundle subgraph subgroup of finite subgroup of G subset subtree Suppose surjective theorem Tits system topology torsion-free tree of groups vector bundle vert vertex whence ye edge