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Algebraic Homotopy

Part of Cambridge Studies in Advanced Mathematics

  • Author: Hans Joachim Baues, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig
  • Date Published: March 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521055314

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  • This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.

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    Product details

    • Date Published: March 2008
    • format: Paperback
    • isbn: 9780521055314
    • length: 488 pages
    • dimensions: 228 x 151 x 27 mm
    • weight: 0.726kg
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    List of symbols
    1. Axioms for homotopy theory and examples of cofibration categories
    2. Homotopy theory in a cofibration category
    3. The homotopy spectral sequences in a cofibration category
    4. Extensions, coverings and cohomology groups of a category
    5. Maps between mapping cones
    6. Homotopy theory of CW-complexes
    7. Homotopy theory of complexes in a cofibration category
    8. Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories
    9. Homotopy theory of reduced complexes
    Bibliography
    Index.

  • Author

    Hans Joachim Baues, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig

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