ETH Zurich

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

Journal
Volume 42 (1996)
Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Front matter
Table of Contents 1
Front matter 2
Article: LA CONJECTURE abc 3
Chapter: 1. Introduction 3
Chapter: 2. La conjecture abc 4
Chapter: 3. Applications de la conjecture abc 6
Chapter: 4. A LA RECHERCHE DE FORMES EFFECTIVES 15
Chapter: 5. GÉNÉRALISATIONS 20
Bibliography 22
Article: DOUBLE VALUED REFLECTION IN THE COMPLEX PLANE 25
Chapter: Introduction 25
Chapter: 1. Double valued reflection 26
Chapter: 2. Conic sections 29
Chapter: 3. The intrinsic theory: genus zero 33
Chapter: 4. Riemann maps 36
Chapter: 5. INVOLUTIONS ON A TORUS 40
Chapter: 6. Embedding of tori 43
Chapter: 7. A RECTANGULAR LATTICE 46
Bibliography 48
Article: KLYACHKO'S METHODS AND THE SOLUTION OF EQUATIONS OVER TORSION-FREE GROUPS 49
Abstract 49
Chapter: 1. Introduction 50
Chapter: 2. The crash theorems 52
Chapter: 3. TWO TRANSVERSALITY LEMMAS 57
Chapter: 4. Application to the Kervaire problem 61
Chapter: 5. The general case 67
Chapter: 6. Further Applications 71
Bibliography 73
Article: CENTRALISERS IN THE BRAID GROUP AND SINGULAR BRAID MONOID 75
Abstract 75
Chapter: 1. Introduction and Basic Definitions 75
Chapter: 2. Commutation and stabilisers 80
Chapter: 3. Proof of Theorem 2.2 82
Chapter: 4. Centralisers of braid subgroups 84
Chapter: 5. The singular braid monoid and the map η 87
Chapter: 6. Results regarding injectivity of η 89
Chapter: 7. Centralisers in $SB_n$ 94
Bibliography 95
Article: MOYENNES SUR CERTAINS ENSEMBLES DE DIVISEURS D'UN ENTIER 97
Abstract 97
Chapter: 1. Introduction 97
Chapter: 2. Propriétés arithmétiques de $\bar{f}$, $\hat{f}$ et $\tilde{f}$ 100
Chapter: 3. Valeurs moyennes de $\bar{f}$, $\hat{f}$ et $\tilde{f}$ 106
Chapter: 4. Mesure de l'écart entre f et les moyennes $\bar{f}$, $\hat{f}$ et $\tilde{f}$ 113
Chapter: 5. GÉNÉRALISATIONS ET EXEMPLES 115
Bibliography 122
Article: EMPILEMENTS DE CERCLES ET REPRÉSENTATIONS CONFORMES: une nouvelle preuve du théorème de Rodin-Sullivan 125
Chapter: I. Introduction 125
Chapter: II. Le Théorème de Rodin-Sullivan : ÉNONCÉ ET SCHÉMA DE LA PREUVE 126
Chapter: IV. Estimations à priori des rayons 135
Chapter: V. Changement de variable 139
Chapter: VI. Inégalité de Harnack 142
Chapter: VII. Commentaires 149
Chapter: 1. Sur l'inégalité de Harnack 149
Chapter: 2. Sur le théorème de Rodin-Sullivan 150
Bibliography 151
Article: UNIFORM DISTRIBUTION ON DIVISORS AND BEHREND SEQUENCES 153
Chapter: 1. DEFINITIONS AND BASIC RESULTS 153
Chapter: 2. Functions of moderate growth 164
Chapter: 3. Functions of excessive growth: the case $f(d) = d^\alpha$ 174
Chapter: 4. FUNCTIONS OF EXCESSIVE GROWTH : THE CASE f(d) =θd 180
Chapter: §5. Additive functions 190
Chapter: 6. Metric results 193
Bibliography 196
Rubric: BULLETIN BIBLIOGRAPHIQUE 1
Back matter
Back matter
Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
Front matter
Article: ON THE GAUSS-BONNET FORMULA FOR LOCALLY SYMMETRIC SPACES OF NONCOMPACT TYPE 201
Abstract 201
Chapter: Introduction 201
Chapter: 1. The formula of Allendoerfer and Weil 203
Chapter: 2. An exhaustion of locally symmetric spaces 204
Chapter: 2.1. Reduction theory and geometry at infinity 204
Chapter: 2.2. An exhaustion by polyhedra 207
Chapter: 3. ESTIMATES FOR THE BOUNDARY SUBPOLYHEDRA 209
Chapter: 4. A NEW PROOF OF THE GAUSS-BONNET FORMULA 212
Bibliography 213
Article: INTRODUCTORY NOTES ON RICHARD THOMPSON'S GROUPS 215
Chapter: §1. Introduction to F 216
Chapter: §2. Tree diagrams 218
Chapter: §3. Presentations for F 225
Chapter: §4. Further properties of F 227
Chapter: §5. Thompson's group T 233
Chapter: §6. Thompson's group V 240
Chapter: §7. Piecewise integral projective structures 248
Bibliography 254
Article: SQUARE-FREE TOWER OF HANOI SEQUENCES 257
Abstract 257
Chapter: 0. Square-free strings and the Olive sequence 257
Chapter: 1. A FINITE ALPHABET 260
Chapter: 2. Smaller alphabets 262
Bibliography 263
Article: CHARACTERISTIC CLASSES, ELLIPTIC OPERATORS AND COMPACT GROUP ACTIONS 265
Chapter: 0. Introduction 265
Chapter: 1. CHARACTERISTIC CLASSES AND MULTIPLICATIVE SEQUENCES 266
Chapter: 2. The index of an elliptic complex 271
Chapter: 3. The Lefschetz fixed point formula 277
Chapter: 4. The Lefschetz Theorem for foliated manifolds 282
Chapter: 5. Group Actions and the Lefschetz Theorem 287
Chapter: 6. The Rigidity Theorem of Witten 290
Bibliography 292
Article: BARBIER'S THEOREM FOR THE SPHERE AND THE HYPERBOLIC PLANE 295
Chapter: 1. Introduction 295
Chapter: 2. Curves of constant width in the euclidean plane 297
Chapter: 3. Geodesic parallel coordinates 302
Chapter: 4. Proof of the main results 307
Bibliography 308
Article: SYSTEMS OF CURVES ON A CLOSED ORIENTABLE SURFACE 311
Chapter: 1. Introduction 311
Chapter: 2. Necessary conditions 315
Chapter: 3. SUFFICIENCY FOR A SINGLE HOMOLOGY CLASS 317
Chapter: 4. SUFFICIENCY FOR INDEPENDENT HOMOLOGY CLASSES 319
Chapter: 5. Disjoint simple closed curves on a planar surface 320
Chapter: 6. SUFFICIENCY IN THEOREM 3 324
Chapter: 7. Various instructive examples 332
Chapter: 8. Some Final Observations 335
Bibliography 339
Article: THE ZERO-IN-THE-SPECTRUM QUESTION 341
Abstract 341
Chapter: 1. Introduction 341
Chapter: 2. DEFINITION OF $L^2$ -COHOMOLOGY 343
Chapter: 3. General Properties of $L^2$-Cohomology 351
Chapter: 4. Very Low Dimensions 358
Chapter: 4.1 One Dimension 358
Chapter: 4.2 Two Dimensions 361
Chapter: 5. Universal Covers 362
Chapter: 5.1 Big and Small Groups 363
Chapter: 5.2 Two and Three Dimensions 365
Chapter: 5.3 Four Dimensions 367
Chapter: 5.4 More Dimensions 369
Chapter: 6. Topologically Tame Manifolds 372
Bibliography 375
Article: IN DEFENSE OF EULER 377
Bibliography 382
Article: FACTOR EQUIVALENCE RESULTS FOR INTEGERS AND UNITS 383
Abstract 383
Chapter: 1. Introduction 383
Chapter: 2. Factorizability and factor equivalence 384
Chapter: 3. Rings of integers 386
Chapter: 4. S-UNITS 387
Chapter: 5. Applications 391
Bibliography 393
Rubric: COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION) 395
Article: UNDERSTANDING THE PROCESSES OF ADVANCED MATHEMATICAL THINKING 395
Chapter: Introduction 395
Chapter: THE DEVELOPMENT OF MATHEMATICAL THINKING 395
Chapter: compression of knowledge in mathematics 398
Chapter: VISUALISING MATHEMATICAL CONCEPTS 400
Chapter: USING SYMBOLISM TO COMPRESS PROCESS INTO CONCEPT 404
Chapter: SEQUENTIAL AND PROCEDURAL COMPRESSION 406
Chapter: transition to formal mathematics 407
Chapter: Can we teach students to "think mathematically" ? 410
Chapter: Reflections on mathematical thinking 412
Bibliography 413
Rubric: BULLETIN BIBLIOGRAPHIQUE 27
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Index
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