ETH Zurich

E–Periodica Schweizer Zeitschriften online. Revues suisses en ligne. Swiss journals online.

Zeitschrift
Volume 34 (1988)
Front matter
Index
Front matter
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE 1
Article: THE SCHUR SUBGROUP OF THE BRAUER GROUP OF A LOCAL FIELD 1
Chapter: K NON-DYADIC 2
Chapter: Remarks 9
Bibliography 10
Article: UNE CARACTÉRISATION DES NORMES EUCLIDIENNES EN DIMENSION FINIE 13
Chapter: Introduction 13
Chapter: I. Groupe des isométries linéaires 14
Chapter: II. La boule unité de L(E) 15
Chapter: III. Application au cas n = 2 18
Bibliography 21
Article: EULER'S FAMOUS PRIME GENERATING POLYNOMIAL AND THE CLASS NUMBER OF IMAGINARY QUADRATIC FIELDS 23
Chapter: Introduction 23
Chapter: A) Quadratic extensions 25
Chapter: B) Rings of integers 26
Chapter: C) Discriminant 27
Chapter: D) Decomposition of primes 27
Chapter: E) Units 32
Chapter: F) The class number 33
Chapter: G) The main theorem 40
Bibliography 42
Article: LE PROBLÈME DE GAUSS SUR LE NOMBRE DE CLASSES 43
Chapter: I. La classification de Gauss des formes quadratiques 44
Chapter: §1. FINITUDE DU NOMBRE DE CLASSES 44
Chapter: §2. Formes quadratiques réduites 45
Chapter: §3. Une méthode élémentaire pour calculer le nombre de classes 47
Chapter: §4. Le groupe des classes 48
Chapter: §5. Lien entre h(-d) et $h(-df^2)$ 51
Chapter: II. Le problème du nombre de classes 52
Chapter: §1. Représentation des entiers par les formes quadratiques 53
Chapter: §2. Fonctions zêta 55
Chapter: §3. Ce que l'on espère sur le comportement de h( —d) 57
Chapter: §4. Minorations non effectives de h(—d) 59
Chapter: §5. Les cas h = 1 et h = 2 60
Chapter: §6. Courbes elliptiques et fonctions L 61
Chapter: §7. Le théorème de Goldfeld 64
Chapter: §8. Le théorème de Gross et Zagier 65
Chapter: §9. Conclusion 66
Article: ON TORRES-TYPE RELATIONS FOR THE ALEXANDER POLYNOMIALS OF LINKS 69
Chapter: §1. Introduction 69
Chapter: §2. Torsions of chain complexes and manifolds 72
Chapter: §3. Algebraic lemmas 74
Chapter: §4. Proof of Theorems 1 and 2 76
Bibliography 82
Article: EXTENSIONS DE MODULES ET COHOMOLOGIE DES GROUPES 83
Chapter: Introduction 83
Chapter: 1. Rappels sur les extensions 83
Chapter: 2. DÉRIVATIONS ET EXTENSIONS 85
Chapter: 3. Le groupe $H^1(G;A)$ 87
Chapter: 4. Le groupe $H^2(G;A)$ 93
Article: ABOUT THE PROOFS OF CALABI'S CONJECTURES ON COMPACT KÄHLER MANIFOLDS 107
Abstract: Abstract 107
Chapter: 0. Introduction 107
Chapter: 1. The Monge-Ampère equation 108
Chapter: 2. A Topological Lemma 110
Chapter: 3. Local inversion 111
Chapter: 4. Properness 111
Chapter: 5. A PRIORI ESTIMATES: THE ORIGINAL WAY 114
Chapter: 6. Coordinate free tensor calculus 114
Chapter: 7. HIGHER ORDER A PRIORI ESTIMATES: GENERALITIES 115
Chapter: 8. A PRIORI ESTIMATES OF ORDER FOUR 118
Chapter: 9. A PRIORI ESTIMATES OF ORDER FIVE AND MORE 120
Chapter: 10. The analytic point of view 121
Bibliography 121
Article: QUILLEN'S THEOREM ON BUILDINGS AND THE LOOPS ON A SYMMETRIC SPACE 123
Abstract: Abstract 123
Chapter: §1. Notation and Preliminaries 128
Chapter: §2. Topological Buildings 134
Chapter: §3. Loop Groups 142
Chapter: §4. Quillen's Theorem for Loop Groups 144
Chapter: §5. The Loops on a Symmetric Space 147
Chapter: §6. Examples 152
Chapter: §7. Bott Periodicity 158
Appendix: §8. Appendix : Real Forms and the generalized bruhat decomposition 161
Bibliography 165
Article: ISOCLINIC n-PLANES IN $R^{2n}$ AND THE HOPF-STEENROD SPHERE BUNDLES $S^{2n-1} \rightarrow S^n,\quad n=2,4,8$ 167
Chapter: 0. Introduction 167
Chapter: 1. Some results on isoclinic n-PLANES in $R^{2n}$ 168
Chapter: 2. SOME FURTHER RESULTS 173
Chapter: 3. The sphère bundles $S^{2n-1} \rightarrow \Phi_n, \quad n=2,4,or 8$, WITH FIBERS ON MUTUALLY ISOCLINIC n-PLANES IN $R^{2n}$ 181
Chapter: 4. A UNIFIED TREATMENT OF THE THREE HOPF-STEENROD BUNDLES 187
Chapter: 5. COMPARISON OF OUR BUNDLES WITH THE HOPF-STEENROD BUNDLES 194
Appendix: Appendix 1. The Cayley numbers 200
Appendix: Appendix 2. The Hopf fibering and mutually isoclinic planes 201
Bibliography 204
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION) 205
Article: THE POPULARIZATION OF MATHEMATICS 205
Chapter: 1. A GENERAL FRAMEWORK: NEEDS AND METHODS FOR THE POPULARIZATION OF SCIENCE 206
Chapter: 2. Spécial features of the popularization of mathematics 207
Chapter: 3. The methods of popularization 210
Chapter: Call for papers 212
Chapter: Previous ICMI Studies 213
Article: THE THEORY OF GRÖBNER BASES 215
Chapter: Introduction 215
Chapter: 1. Notations and Definitions 216
Chapter: 2. The Division Algorithm 220
Chapter: 3. Construction of Gröbner Bases 223
Chapter: 4. Application to Systems of Algebraic Equations 228
Chapter: 5. Application to a Geometric Problem 230
Bibliography 231
Article: GEODESICS IN THE UNIT TANGENT BUNDLE OF A ROUND SPHERE 233
Chapter: 1. Geometry of the unit tangent bundle 235
Chapter: 2. Geodesics in $US^2$ 238
Chapter: 3. Helices in $S^3$ 239
Chapter: 4. SASAKI'S EQUATIONS 240
Chapter: 5. Proof of the Fundamental Constraint 243
Bibliography 246
Article: THE EULER CLASS OF ORTHOGONAL RATIONAL REPRESENTATIONS OF FINITE GROUPS 247
Chapter: 1. Invariant Bilinear Forms 248
Chapter: 2. Orthogonal representations of p-groups 249
Chapter: 3. Proof of the main theorem 252
Bibliography 253
Article: UNE THÉORIE DE DENJOY DES MARTINGALES DYADIQUES 255
Chapter: problème 255
Chapter: solution: totalisation dyadique 257
Chapter: Commentaires 261
Appendix: Appendice: distribution de la fonction f 263
Chapter: CITATIONS ET PASTICHE 266
Bibliography 268
Article: AN ELEMENTARY PROOF OF THE STRUCTURE THEOREM FOR CONNECTED SOLVABLE AFFINE ALGEBRAIC GROUPS 269
Abstract: Abstract 269
Rubric 270
Bibliography 273
Article: KALUZA-KLEIN APPROACH TO HYPERBOLIC THREE-MANIFOLDS 275
Chapter: §1. Introduction 275
Chapter: §2. CONFORMAL COMPACTIFICATIONS AND THEIR TOPOLOGY 277
Chapter: §3. Classification of Γ with $dim_H\Lambda(\Gamma)\leq 1$ 284
Chapter: §4. HODGE THEORY FOR HYPERBOLIC 3-MANIFOLDS 287
Chapter: §5. Monopoles and Instantons 291
Chapter: §6. Twistor spaces 295
Chapter: §7. Atiyah-Ward ansatzes, summing 't Hooft solutions and elsenstein series 305
Bibliography 310
Article: SOME ALMOST HOMOGENEOUS GROUP ACTIONS ON SMOOTH COMPLETE RATIONAL SURFACES 313
Chapter: §1. Minimal embeddings: définitions and preliminary remarks 314
Chapter: §2. The minimal B/Γ-embeddings 317
Chapter: §3. Application to SL(2)-embeddings 331
Bibliography 332
Article: REPRÉSENTATIONS ET TRACES DES ALGÈBRES DE HECKE POLYNÔME DE JONES-CONWAY 333
Chapter: §0. Introduction 333
Chapter: §1. Une description du polynôme de Jones-Conway 336
Chapter: §2. Représentations des algèbres de Hecke 340
Chapter: §3. Traces des algèbres de Hecke 342
Chapter: §4. La trace T 345
Chapter: §5. La trace de Jones-Ocneanu 348
Chapter: §6. Une généralisation du polynôme de Jones-Conway 349
Bibliography 355
Article: GLOBAL CONSTRUCTION OF THE NORMALIZATION OF STEIN SPACES 357
Chapter: Introduction 357
Chapter: 1. Example of a Stein space X with $\widetilde{O(X)} \neq O(\tilde{X})$ 358
Chapter: 2. Construction of $O(\tilde{X})$ from O(X) for Stein spaces X 360
Chapter: 3. Applications 361
Bibliography 363
Article: LES ÉQUATIONS DIFFÉRENTIELLES ONT 350 ANS 365
Chapter: problèmes de Debeaune 365
Chapter: «Discorsi» de Galilée 366
Chapter: Newton 367
Chapter: Solution du premier problème de Debeaune 369
Chapter: problème de l'isochrone 370
Chapter: caténaire 371
Chapter: tractrice 373
Chapter: L'ÉQUATION DIFFÉRENTIELLE «DE BERNOULLI» 374
Chapter: Brachystochrone 375
Chapter: PROBLÈMES ISOPÉRIMÉTRIQUES 377
Chapter: Euler et Lagrange 379
Chapter: Problèmes isopérimétriques, suite 380
Chapter: Epilogue 381
Chapter: Exercices 382
Bibliography 384
Article: LES GRANDS THÈMES DE FRANÇOIS CHÂTELET 387
Chapter: 1. Variétés de Severi-Brauer 387
Chapter: 1.1. Avant Châtelet. 387
Chapter: 1.2. La contribution de F. Châtelet [1943a] [1943b] [1944]. 389
Chapter: 1.3. Après les travaux de Châtelet. 391
Chapter: 1.4. Importance des variétés de Severi-Brauer. 391
Chapter: 2. Courbes de genre 1 392
Chapter: 2.1. Avant Châtelet. 392
Chapter: 2.2. La contribution de Châtelet [1938] [1941] [1946a] [1947a]. 393
Chapter: 2.3. Après Châtelet. 395
Chapter: 2.4. Points de torsion. 395
Chapter: 3. Surfaces cubiques 396
Chapter: 3.1. Avant Châtelet. 396
Chapter: 3.2. La contribution de Châtelet [1953] [1954 a] [1954b] [1958] [1959b] [1966]. 397
Chapter: 3.3. Après Châtelet. 399
Chapter: ARTICLES DE FRANÇOIS CHÂTELET 401
Bibliography 403
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Rubric: BULLETIN BIBLIOGRAPHIQUE 41
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