Mathematical Survey Lectures 19432004 [electronic resource] / by Beno Eckmann.

LidȨe de dimension -- Topologie und Algebra -- Complex-analytic manifolds -- Homotopie et dualitȨ -- Groupes dhomotopie et dualitȨ -- Homotopy and cohomology theory -- Simple homotopy type and categories of fractions -- Some recent developments in the homology theory of groups -- PoincarȨ duality groups of dimension two are surface groups -- Continuous solutions of linear equations An old problem, its history, and its solution -- Mathematics: Questions and Answers -- Hurwitz-Radon matrices revisited: From effective solution of the Hurwitz matrix equations to Bott periodicity -- Birth of fibre spaces, and homotopy -- 4-Manifolds, group invariants, and ? 2-Betti numbers -- The Euler characteristic a few highlights in its long history -- Topology, algebra, analysis relations and missing links -- to ?2-methods in topology: Reduced ?2-homology, harmonic chains, ?2-Betti numbers -- Die Zukunft der Mathematik Ein Rȭckblick auf Hilberts programmatischen Vortrag vor 100 Jahren -- Kolmogorov and contemporary mathematics -- Is algebraic topology a respectable field? -- Social choice and topology. A case of pure and applied mathematics.

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.

ZDB-2-SMA