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Algebraic Homotopy : Cambridge Studies in Advanced Mathematics - Hans-Joachim Baues

Algebraic Homotopy

Cambridge Studies in Advanced Mathematics

By: Hans-Joachim Baues, B. Bollobas (Editor), W. Fulton (Editor), A. Katok (Editor), F. Kirwan (Editor)

Hardcover

Published: 31st March 1989
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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.

Preface
Introduction
List of symbols
Axioms for homotopy theory and examples of cofibration categories
Homotopy theory in a cofibration category
The homotopy spectral sequences in a cofibration category
Extensions, coverings and cohomology groups of a category
Maps between mapping cones
Homotopy theory of CW-complexes
Homotopy theory of complexes in a cofibration category
Homotopy theory of Postnikov towers and the Sullivan-de Rham equivalence of rational homotopy categories
Homotopy theory of reduced complexes
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521333764
ISBN-10: 0521333768
Series: Cambridge Studies in Advanced Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 488
Published: 31st March 1989
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 3.2
Weight (kg): 0.88