2006

Mathematical Survey Lectures 1943–2004

Authors:

ISBN: 978-3-540-33790-4 (Print) 978-3-540-33791-1 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages i-viii

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    Book Chapter

    Pages 1-15

    L’idée de dimension

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    Pages 17-26

    Topologie und Algebra

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    Pages 27-34

    Complex-analytic manifolds

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    Pages 35-47

    Homotopie et dualité

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    Pages 49-59

    Groupes d’homotopie et dualité

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    Pages 61-75

    Homotopy and cohomology theory

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    Pages 77-91

    Simple homotopy type and categories of fractions

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    Pages 93-107

    Some recent developments in the homology theory of groups

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    Book Chapter

    Pages 109-119

    Poincaré duality groups of dimension two are surface groups

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    Book Chapter

    Pages 121-134

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

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    Book Chapter

    Pages 135-140

    Mathematics: Questions and Answers

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    Book Chapter

    Pages 141-153

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

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    Book Chapter

    Pages 155-165

    Birth of fibre spaces, and homotopy

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    Pages 167-175

    4-Manifolds, group invariants, and 2-Betti numbers

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    Book Chapter

    Pages 177-188

    The Euler characteristic — a few highlights in its long history

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    Book Chapter

    Pages 189-196

    Topology, algebra, analysis — relations and missing links

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    Book Chapter

    Pages 197-233

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

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    Book Chapter

    Pages 235-240

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

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    Book Chapter

    Pages 241-244

    Kolmogorov and contemporary mathematics

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    Book Chapter

    Pages 245-256

    Is algebraic topology a respectable field?

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