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Mathematical Survey Lectures 1943-2004

  • Book
  • © 2006

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Authors:
  1. Beno Eckmann

    1. Institute for Mathematical Research, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. L’idée de dimension

    Pages 1-15

  3. Topologie und Algebra

    Pages 17-26

  4. Complex-analytic manifolds

    Pages 27-34

  5. Homotopie et dualité

    Pages 35-47

  6. Groupes d’homotopie et dualité

    Pages 49-59

  7. Homotopy and cohomology theory

    Pages 61-75

  8. Simple homotopy type and categories of fractions

    Pages 77-91

  9. Some recent developments in the homology theory of groups

    Pages 93-107

  10. Poincaré duality groups of dimension two are surface groups

    Pages 109-119

  11. Continuous solutions of linear equations — An old problem, its history, and its solution

    Pages 121-134

  12. Mathematics: Questions and Answers

    Pages 135-140

  13. Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity

    Pages 141-153

  14. Birth of fibre spaces, and homotopy

    Pages 155-165

  15. 4-Manifolds, group invariants, and ℓ 2-Betti numbers

    Pages 167-175

  16. The Euler characteristic — a few highlights in its long history

    Pages 177-188

  17. Topology, algebra, analysis — relations and missing links

    Pages 189-196

  18. Introduction to ℓ2-methods in topology: Reduced ℓ2-homology, harmonic chains, ℓ2-Betti numbers

    Pages 197-233

  19. Die Zukunft der Mathematik Ein Rückblick auf Hilberts programmatischen Vortrag vor 100 Jahren

    Pages 235-240

  20. Kolmogorov and contemporary mathematics

    Pages 241-244
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Keywords

About this book

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.

Reviews

From the reviews:

"The book under review is a collection of twenty-one survey or expository lectures given by its distinguished author during the period 1943 and 2004 … . All are (broadly) in the fields of topology, algebra and differential geometry. … Students will learn an important and substantial swathe of 20th century geometrical mathematics by carefully reading this delightful book." (Ross Geoghegan, Mathematical Reviews, Issue 2008 c)

"The papers are arranged chronologically, and cover more than 60 years of work. … The collection is rounded out by a couple essays on the place of mathematics in culture and its future. … I heartily recommend adding it to your library." (John McCleary, MAA Online, February, 2009)

Authors and Affiliations

  • Institute for Mathematical Research, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland

    Beno Eckmann

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