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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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1
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Front matter
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2
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Article: HIGHER EULER CHARACTERISTICS (I)
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3
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Abstract
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3
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Chapter: Introduction
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3
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Chapter: 1. Three définitions of the first order Euler characteristic
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5
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Chapter: 2. Discussion of Définition $A_1$
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9
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Chapter: 3. SOME CALCULATIONS
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15
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Chapter: 4. $S^1$-FIBRATIONS
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20
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Chapter: 5. A HIGHER ANALOG OF GOTTLIEB'S THEOREM
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25
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Chapter: 6. Mapping Tori
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31
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Chapter: 7. More on groups of type F
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43
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Chapter: 8. OUTER AUTOMORPHISMS OF GROUPS OF TYPE F
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47
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Chapter: 9. Trace formulae for homological intersections
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50
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Chapter: 10. Proofs of Theorems 1.1 and 1.5
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58
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Bibliography
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61
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Article: STRUCTURE CONFORME AU BORD ET FLOT GÉODÉSIQUE D'UN CAT(- 1)-ESPACE
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63
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Abstract
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63
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Abstract
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63
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Abstract: Sommaire
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63
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Chapter: Introduction
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64
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Chapter: 1. Préliminaires
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65
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Chapter: 1.1. GÉNÉRALITÉS SUR LES ESPACES MÉTRIQUES
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65
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Chapter: 1.2. Espaces hyperboliques géodésiques
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67
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Chapter: 1.3. $CAT(-b^2)$-espaces
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68
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Chapter: 1.4. Bord d'un espace hyperbolique
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69
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Chapter: 1.5. MÉTRIQUES VISUELLES SUR δX
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70
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Chapter: 1.6. Action au bord des quasi-isométries
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72
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Chapter: 1.7. Groupes hyperboliques
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77
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Chapter: 1.8. Groupes quasi-convexes
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78
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Chapter: 2. Structure conforme sur le bord d'un CAT(-1)-espace Ensemble limite et flot géodésique associés à une action quasi-convexe
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80
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Chapter: 2.0. Introduction
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80
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Chapter: 2.1. Fonctions de Busemann
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82
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Chapter: 2.2. Distances horosphériques
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82
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Chapter: 2.3. Horosphères
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82
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Chapter: 2.4. Produit de Gromov de deux éléments de δX
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83
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Chapter: 2.5. Une famille de métriques visuelles sur δX
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84
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Chapter: 2.6. Structure conforme sur δX
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89
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Chapter: 2.7. Mesures conformes sur l'ensemble limite d'un groupe quasiconvexe
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92
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Chapter: 2.8. Flot géodésique associé à une action quasi-convexe
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93
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Chapter: 2.9. Le paramétrage de Hopf de $E, \Phi_T$
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95
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Chapter: 2.10. Mesure d'entropie maximale
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96
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Chapter: 2.11. Preuve du théorème 2.0.1.
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97
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Bibliography
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101
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Article: CONCERNING A REAL-VALUED CONTINUOUS FUNCTION ON THE INTERVAL WITH GRAPH OF HAUSDORFF DIMENSION 2
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103
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Abstract
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103
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Chapter: 0. Introduction
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103
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Chapter: 1. A Lemma about mass distribution
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105
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Chapter: 2. A Lemma about mass distribution AND SUCCESSIVE TRANSLATIONS
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105
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Chapter: 3. Hausdorff measure, net measure and Hausdorff dimension
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106
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Chapter: 4. Mass distribution and Hausdorff dimension
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106
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Chapter: 5. The main result
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107
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Bibliography
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109
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Article: FORMES QUADRATIQUES DEVENANT ISOTROPES SUR UNE EXTENSION
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111
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Chapter: Introduction
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111
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Chapter: 1. Rappels et notations (voir [4] ou [7])
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111
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Chapter: 2. Critères
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112
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Chapter: 3. DÉMONSTRATION DU THÉORÈME 1
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113
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Chapter: 4. Extensions finies – le théorème de Springer
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114
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Chapter: 5. Extensions finies formulations équivalentes des critères du §2
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115
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Chapter: 6. Corps de fonctions d'une quadrique
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117
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Chapter: 7. Applications
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118
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Bibliography
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121
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Article: CHAOTIC GROUP ACTIONS
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123
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Abstract
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123
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Chapter: 1. Introduction
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123
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Chapter: 2. Chaos Equals Residual Finiteness
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124
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Chapter: 3. Constructions of Chaotic Group Actions
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127
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Chapter: 4. Manifolds That Admit Chaotic Group Actions
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128
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Chapter: 5. Other Questions
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131
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Bibliography
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132
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Article: UNE CARACTÉRISATION DU PLAN PROJECTIF COMPLEXE
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135
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Chapter: Introduction
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135
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Bibliography
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139
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Article: JACOBI SUMS AND STICKELBERGER'S CONGRUENCE
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141
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Abstract
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141
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Chapter: Introduction
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141
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Chapter: Proof of Stickelberger's Congruence Via Jacobi Sums
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143
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Chapter: Proof of Jacobi Sum Congruence Via Stickelberger
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148
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Bibliography
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152
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Article: UN THÉORÈME DE RIGIDITÉ POUR LES SURFACES MINIMALES DE $E^3$
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155
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Chapter: 1. Introduction
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155
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Chapter: 2. RÉSULTATS
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156
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Chapter: 3. DÉMONSTRATIONS
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159
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Chapter: 4. Exemples
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172
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Appendix: Annexe I
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176
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Bibliography
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177
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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1
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Back matter
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Back matter
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Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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179
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Front matter
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180
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Article: ON THE COHOMOLOGY OF COMPACT LIE GROUPS
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181
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Abstract
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181
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Chapter: 1. Introduction
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181
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Chapter: 2. Basic material
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183
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Chapter: 3. Invariant Theory
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184
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Chapter: 4. Invariant Differential Forms
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189
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Chapter: 5. The cohomology of flag manifolds
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190
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Chapter: 6. The cohomology of a Lie group
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194
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Bibliography
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199
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Article: SYNTHETIC PROJECTIVE GEOMETRY AND POINCARÉ'S THEOREM ON AUTOMORPHISMS OF THE BALL
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201
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Chapter: 1. Introduction
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201
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Chapter: 2. The local collineation theorem
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203
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Chapter: 3. The Poincaré-Tanaka and Chern-Ji theorems
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211
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Bibliography
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214
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Article: PLURIDIMENSIONAL ABSOLUTE CONTINUITY FOR DIFFERENTIAL FORMS AND THE STOKES FORMULA
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217
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Abstract: Table of Contents
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217
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Chapter: Introduction
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217
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Chapter: 1. INTEGRAL AND ABSOLUTE CONTINUITY AND THE LOCAL PROBLEM
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221
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Chapter: 2. Characterizations of the pluridimensional absolute continuity
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226
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Chapter: 3. A MAXIMUM PRINCIPLE
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229
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Chapter: 4. The global Stokes formula for simple Lipschitz domains in $R^n$
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233
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Chapter: 5. The global form of the Stokes formula on $C^1$ manifolds
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237
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Chapter: 6. Tests for the equalities du =f and $\bar{\delta}u =f$ in the weak sense
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240
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Chapter: 7. SOME APPLICATIONS TO HYPERCOMPLEX FUNCTION THEORY
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248
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Bibliography
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Article: BIRAPPORT ET GROUPOÏDES
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Chapter: 1. Groupoïdes et espaces projectifs
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Chapter: 1.1 Présentation d'un groupoïde par générateurs et relations
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257
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Chapter: 1.2 Le groupoïde des points de $P^n(F)$
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259
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Chapter: 1.3 Preuve du théorème 2
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262
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Chapter: 2. Groupoïdes et Grassmanniennes
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264
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Chapter: 2.1 Présentation par générateurs et relations
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264
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Chapter: 2.2 Invariants projectifs de quadruplets de sous-espaces de dimension l-1 de $P^{2l-1}(F)$
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268
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Chapter: 3. HOMOLOGIE DU GROUPE LINÉAIRE ET GÉOMÉTRIE PROJECTIVE
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270
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Chapter: 3.1 HOMOLOGIE DU GROUPE MULTIPLICATIF D'UN CORPS ET ESPACE PROJECTIF INFINI
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270
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Chapter: 3.2 Homologie du groupe linéaire et grassmanniennes infinies
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274
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Chapter: 4. MULTIRAPPORTS
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276
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Chapter: 4.1 GROUPOÏDES ET n-RAPPORTS
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276
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Chapter: 4.2 Remarques sur un invariant de Goncharov
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277
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Bibliography
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280
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Article: RATIONALITY PROBLEMS FOR K-THEORY AND CHERN-SIMONS INVARIANTS OF HYPERBOLIC 3-MANIFOLDS
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281
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Chapter: 1. Hyperbolic 3-manifolds and Bloch groups
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284
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Chapter: 2. Borel's Theorem
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286
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Chapter: 3. Proof and generalization of Theorem B
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289
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Chapter: 4. Milnor's and Ramakrishnan's conjectures
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291
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Chapter: 5. Chern-Simons invariants and the regulator map
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294
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Bibliography
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295
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Article: CUBIC FORMS AND COMPLEX 3-FOLDS
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297
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Abstract
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297
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Chapter: Introduction
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297
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Chapter: 1. Topological classification of certain 6-manifolds
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299
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Chapter: 1.1 HOMEOMORPHISM TYPES AND $C^\infty$-STRUCTURES
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299
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Chapter: 1.2 Homotopy types
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301
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Chapter: 2. Realization of cubic forms
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303
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Chapter: 2.1 COHOMOLOGY RINGS OF 6-MANIFOLDS
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304
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Chapter: 2.2 Homotopy types with a given cohomology ring
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306
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Chapter: 3. Algebra and arithmetic of cubic forms
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309
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Chapter: 3.1 Algebraic properties of cubic forms
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309
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Chapter: 3.2 The GIT quotient $S^3 H_C^v//SL(H_C)$
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311
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Chapter: 3.3 Arithmetical aspects
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313
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Chapter: 4. Invariants of complex 3-folds
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315
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Chapter: 4.1 Chern numbers of almost complex structures
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315
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Chapter: 4.2 Standard constructions
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318
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Chapter: 4.3 EX AMPLES OF 1-CONNECTED NON-KÄHLERIAN 3-FOLDS
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320
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Chapter: 5. Complex 3-folds with small $b_2$
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324
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Chapter: 5.1 3-folds with $b_2 = 1$
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325
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Chapter: 5.2 3-folds with $b_2 = 2$
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326
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Chapter: 5.3 3-folds with $b_2 \geq 3$
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328
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Bibliography
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330
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Article: DENSITÉ DANS DES FAMILLES DE RÉSEAUX. APPLICATION AUX RÉSEAUX ISODUAUX
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335
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Abstract
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335
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Abstract
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335
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Chapter: 1. Introduction
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335
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Chapter: 2. Exemples
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337
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Chapter: 3. Perfection et eutaxie
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340
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Chapter: 4. EXTRÉMALITÉ DANS F
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343
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Chapter: 5. RÉSULTATS DE CLASSIFICATION
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348
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Chapter: 6. ISODUALITÉ
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349
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Chapter: 7. RÉSEAUX ISODUAUX ORTHOGONAUX ET SYMPLECTIQUES
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356
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Chapter: 8. Classification des réseaux isoduaux de petite dimension
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360
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Bibliography
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364
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Rubric: BULLETIN BIBLIOGRAPHIQUE
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35
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Back matter
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Front matter
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Index
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Back matter
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Back matter
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Back matter
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