Algebraic homotopy
Author(s)
Bibliographic Information
Algebraic homotopy
(Cambridge studies in advanced mathematics, 15)
Cambridge University Press, 1989, c1988
- : hard
- : pbk
Available at 67 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Bibliography: p. [455]-460
Includes index
Description and Table of Contents
Description
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.
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.
by "Nielsen BookData"