Mathematical Survey Lectures 1943-2004 (eBook)

Beno Eckmann 4
Preface 7
Table of Contents 8
L'idee de dimension 9
Topologie und Algebra 25
Complex-analytic manifolds 35
Homotopie et dualite 43
Groupes d'homotopie et dualite 56
Homotopy and cohomology theory 67
Simple homotopy type and categories of fractions 82
Some recent developments in the homology theory of groups 97
Poincare duality groups of dimension two are surface groups 112
Continuous solutions of linear equations - An old problem, its history, and its solution 123
Mathematics: Questions and Answers 137
Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity 143
Birth of fibre spaces, and homotopy 156
4- Manifolds5 group invariants, and 4- Betti numbers 167
The Euler characteristic - a few highhghts in its long history 176
Topology, algebra, analysis relations and missing links 188
Introduction to ^- methods in topology: Reduced 4- homology, harmonic chains, 4- Betti numbers 196
Die Zukunft der Mathematik Ein Riickblick auf Hilberts programmatischen Vortrag vor 100 Jahren 233
Kolmogorov and contemporary mathematics 239
Is algebraic topology a respectable field? 243
Social choice and topology. A case of pure and applied mathematics 255