Eckmann Mathematical Survey Lectures 1943-2004

1. Auflage 2006
ISBN: 978-3-540-33791-1
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 266 Seiten

In my long professional life as a mathematician I have had to deliver various survey lectures. They were of different character according to the occasion. A selected number are reproduced in this volume. They were, with few exceptions, printed in books or in periodicals, and are reproduced here without any modification. I started as a student at the ETH Zurich in 1935 and have spent my working Ufe there, with the exception of the period 1942-1948 (lecturer then associate professor at the University of Lausanne) and 1947 and 1951/52 (Institute for Advanced Study Princeton). In 1948 I was appointed as a professor at the ETH; I retired in 1984 and have since then been professor emeritus. The surveys in this volume are lectures given at congresses and workshops, at international congresses of mathematicians (plenary or section lectures), and at special occasions like birthdays or commemorations. They all reflect the special interests of the respective times. Although they are in fields of topology, algebra and differential geometry they reveal the big changes mathematics has undergone over the years from 1943 to 2004. New thinking has been developed; it has created new problems, or simply has let old problems appear in a new light.

Autoren/Hrsg.

Eckmann, Beno

Inhaltsverzeichnis

1;Beno Eckmann;4
2;Preface;7
3;Table of Contents;8
4;L'idee de dimension;9
5;Topologie und Algebra;25
6;Complex-analytic manifolds;35
7;Homotopie et dualite;43
8;Groupes d'homotopie et dualite;56
9;Homotopy and cohomology theory;67
10;Simple homotopy type and categories of fractions;82
11;Some recent developments in the homology theory of groups;97
12;Poincare duality groups of dimension two are surface groups;112
13;Continuous solutions of linear equations - An old problem, its history, and its solution;123
14;Mathematics: Questions and Answers;137
15;Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity;143
16;Birth of fibre spaces, and homotopy;156
17;4- Manifolds5 group invariants, and 4- Betti numbers;167
18;The Euler characteristic - a few highhghts in its long history;176
19;Topology, algebra, analysis relations and missing links;188
20;Introduction to ^- methods in topology: Reduced 4- homology, harmonic chains, 4- Betti numbers;196
21;Die Zukunft der Mathematik Ein Riickblick auf Hilberts programmatischen Vortrag vor 100 Jahren;233
22;Kolmogorov and contemporary mathematics;239
23;Is algebraic topology a respectable field?;243
24;Social choice and topology. A case of pure and applied mathematics;255