ETH Zurich
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L'Enseignement Mathématique

Volume 29 (1983)
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Table of Contents
Front matter
Index
Front matter
Article: SOME PARADOXICAL SETS WITH APPLICATIONS IN THE GEOMETRIC THEORY OF REAL VARIABLE 1
Chapter: 1. Maneuvering a needle 1
Chapter: 2. Streets in all directions covering null area 2
Chapter: 3. A TOURIST COLONY NOT TO BE RECOMMENDED 3
Chapter: 4. A SMALL TREE WITH MANY FRUITS 3
Chapter: 5. How the Perron tree sprouts 4
Chapter: 6. The solution of the needle problem 8
Chapter: 7. The construction of the Besocovitch set 9
Chapter: 8. The Nikodym set 11
Chapter: 9. Mathematical frivolities? From the Perron tree to the measure of the density 12
Chapter: 10. Another fruit of the Perron tree. A PROBLEM ON DOUBLE FOURIER SERIES 13
Bibliography 14
Article: MANIFOLDS WITH CANONICAL COORDINATE CHARTS : SOME EXAMPLES 15
Chapter: Inversive 2-manifolds 18
Chapter: Affine structures in 2, 3, and 4 dimensions 22
Bibliography 25
Article: GROUPE DE WITT D'UNE ALGÈBRE AVEC INVOLUTION 27
Chapter: §1. RÉDUCTION AU CAS SEMISIMPLE 28
Chapter: §2 Réduction au groupe de Witt hermitien d'un corps gauche 31
Chapter: §3. Présentation du groupe de Witt hermitien d'un corps gauche 37
Article: EXACT SEQUENCES OF WITT GROUPS OF EQUIVARIANT FORMS 45
Bibliography 51
Article: REPRESENTATIONS OF THE SYMMETRIC GROUP, THE SPECIALIZATION ORDER, SYSTEMS AND GRASSMANN MANIFOLDS 53
Abstract: Abstract 53
Abstract: Contents 53
Chapter: 1. Introduction 54
Chapter: 2. SEVERAL MANIFESTATIONS OF THE SPECIALIZATION ORDER 56
Chapter: 3. Grassmann manifolds and classifying vectorbundles 59
Chapter: 4. Schubert Cells 60
Chapter: 5. Interrelations 62
Chapter: 6. Young's rule, the specialization order and nilpotent matrices 65
Chapter: 7. Nilpotent matrices and systems 67
Chapter: 8. VECTORBUNDLES AND SYSTEMS 73
Chapter: 9. Vectorbundles, systems and Schubert cells 76
Chapter: 10. Deformations of representation homomorphisms and subrepresentations 81
Chapter: 11. A FAMILY OF REPRESENTATIONS OF $S_{n+m}$ PARAMETRIZED BY $G_n(C^{n+m})$ 82
Bibliography 85
Article: THE METHOD OF HADAMARD AND DE LA VALLÉE-POUSSIN (ACCORDING TO PIERRE DELIGNE) 89
Abstract: Contents 89
Chapter: Introduction 90
Chapter: Part I: Examples 91
Chapter: Part II: Statement of the theorem 100
Chapter: Part III: Proof of the Main Lemma 114
Bibliography 128
Article: FREE GROUPS IN LINEAR GROUPS 129
Chapter: 1. Early examples 129
Chapter: 2. Statement of Tits' theorem 132
Chapter: 3. Digression on hyperbolic geometry 134
Chapter: 4. Free subgroups of GL(2, R) and of GL(2, C) 135
Chapter: 5. SOME OTHER CASES OF TITS' THEOREM 139
Bibliography 142
Article: DIVISION ALGEBRAS AND THE HAUSDORFF-BANACH-TARSKI PARADOX 145
Appendix: Appendix A 147
Appendix: Appendix B 148
Appendix: Appendix C 149
Bibliography 150
Article: ON FREE SUBGROUPS OF SEMI-SIMPLE GROUPS 151
Chapter: §1. Proof of Theorem B 153
Chapter: §2. Free subgroups with strongly regular elements 157
Chapter: §3. Compact groups. Proof of Theorem A. 161
Chapter: §4. Free group actions with commutative isotropy groups 161
Bibliography 164
Article: KUMMER'S IDEAS ON FERMAT'S LAST THEOREM 165
Bibliography 176
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION) 179
Article: SOME KNOT THEORY OF COMPLEX PLANE CURVES 185
Chapter: §1. Aspects of the "placement problem" for complex plane curves 185
Chapter: §2. A TRIPTYCH 185
Chapter: §3. RÉSUMÉ OF BASIC DEFINITIONS 186
Chapter: §4. Local knot theory in brief 186
Chapter: §5. Global knot theory in brief—the projective case 190
Chapter: §6. Global knot theory in brief—the affine case 193
Chapter: §7. The middle range 195
Bibliography 207
Article: SUR LES SOMMES DE QUATRE CUBES 209
Bibliography 220
Article: THE TOPOLOGY OF REAL ALGEBRAIC SETS 221
Chapter: §0. Introduction 222
Chapter: §1. Resolution of Algebraic Sets 225
Chapter: §2. Nonsingular Algebraic Sets 229
Chapter: §3. Blowing Down 237
Chapter: §4. Isolated Singularities 240
Chapter: §5. Algebraic Structures on P.L. Manifolds 246
Chapter: §6. On classification of Real Algebraic Sets 250
Bibliography 260
Article: MILNOR LATTICES AND GEOMETRIC BASES OF SOME SPECIAL SINGULARITIES 263
Chapter: Introduction 263
Chapter: 1. The Milnor Lattice of a Singularity 264
Chapter: 2. Geometric Bases of the Milnor Lattice 266
Chapter: 3. Milnor Lattices and Weakly Distinguished Bases of Some Special Singularities 269
Chapter: 4. Distinguished Bases for the Bimodular Singularities 273
Bibliography 280
Article: ON POLYLOGARITHMS, HURWITZ ZETA FUNCTIONS, AND THE KUBERT IDENTITIES 281
Chapter: §1. Introduction 281
Chapter: §2. Classical examples 282
Chapter: §3. Continuous Kubert functions 287
Chapter: §4. EXTENDING FROM (0, 1) TO R/Z 292
Chapter: §5. Universal Kubert functions 294
Chapter: §6. On Q-linear relations 300
Appendix: Appendix 1 Relations between polylogarithm and Hurwitz function 306
Appendix: Appendix 2 SOME RELATIVES OF THE GAMMA FUNCTION 309
Appendix: Appendix 3 Volume and the Dehn invariant in hyperbolic 3-space 315
Bibliography 321
Article: PROPOS DES ÉQUATIONS ANTIPELLIENNES 323
Bibliography 327
Article: VANISHING OF COHOMOLOGY WITH COEFFICIENTS IN A LOCALLY FREE SHEAF AND PSEUDOCONVEXITY 329
Chapter: Introduction 329
Bibliography 338
Article: THE CLEBSCH-GORDAN FORMULAS 339
Chapter: 0. Introduction 339
Chapter: 1. SOME REPRESENTATIONS OF $sI_2$ 339
Chapter: 2. The Weyl algebra A 340
Chapter: 3. The theory of the highest weight 342
Chapter: 4. The decomposition of A 342
Chapter: 5. Decomposition of $Hom(V_m, V_{m+n})$ 344
Bibliography 346
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION) 347
Chapter: ICMI NOTES 347
Article: THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION PAST, PRESENT AND FUTURE 348
Rubric
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubric: BULLETIN BIBLIOGRAPHIQUE 45
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