KALUZA-KLEIN APPROACH TO HYPERBOLIC THREE-MANIFOLDS

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