Mathematical Survey Lectures 1943-2004

Beno Eckmann3540337903, 9783540337911, 9783540337904

This collection traces the career of Beno Eckmann, whose work ranges across a broad spectrum of mathematical concepts from topology and differential geometry through homological algebra to group theory. One of our most influential living mathematicians, Eckmann has been associated for nearly his entire professional life with the Swiss Federal Institute of Technology Zurich (ETH), as student, lecturer, professor, and professor emeritus.

The lectures offer a fascinating account of advances in pure mathematics from 1943 to 2004, as new topics and methods are introduced, and gradually become routine. The penultimate lecture is a personal-historical overview of algebraic topology, delivered in connection with the 40-year jubilee of the Institute for Mathematical Research (FIM), which Eckmann founded at ETH in 1964. In the final article, Eckmann looks beyond pure mathematics to consider the application in concrete fields of intellectual enterprise.

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Table of contents :
Title……Page 1
Beno Eckmann – Photo……Page 2
Title page……Page 3
Date-line……Page 4
Dedication……Page 5
Preface……Page 6
Table of Contents……Page 7
L’idee de dimension (1943)……Page 8
Eidgenoessische Technische Hochschule Zuerich, ETHZ – Photo……Page 23
Topologie und Algebra (1943)……Page 24
Complex-analytic manifolds (1950)……Page 34
Homotopie et dualite (1956)……Page 42
Groupes d’homotopie et dualite (1958)……Page 56
Homotopy and cohomology theory (1962)……Page 68
Simple homotopy type and categories of fractions (1970)……Page 84
Some recent developments in the homology theory of groups (1980)……Page 100
Poincare duality groups of dimension two are surface groups (1986)……Page 116
Continuous solutions of linear equations – An old problem, its history, and its solution (1991)……Page 128
Mathematics: Questions and Answers (1994)……Page 142
Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity (1994)……Page 148
Birth of fibre spaces, and homotopy (1996)……Page 162
4-Manifolds, group invariants, and $l_2$-Betti numbers (1997)……Page 174
The Euler characteristic – a few highlights in its long history (1999)……Page 184
Topology, algebra, analysis – relations and missing links (1999)……Page 196
Introduction to $l_2$-methods in topology: Reduced $l_2$-homology, harmonic chains, $l_2$-Betti numbers (2000)……Page 204
Die Zukunft der Mathematik. Ein Ruckblick auf Hilberts programmatischen Vortrag vor 100 Jahren (2000)……Page 242
Kolmogorov and contemporary mathematics (2003)……Page 248
Heinz Hopf and Hermann Weyl – Photo……Page 251
Is algebraic topology a respectable field? (2004)……Page 252
Social choice and topology. A case of pure and applied mathematics (2004)……Page 264
Acknowledgements……Page 273