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(Ebook) Algebraic Homotopy 1st Edition by Hans Joachim Baues ISBN 0521055318 9780521055314

  • SKU: EBN-2005884
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Authors:Hans Joachim Baues
Pages:486 pages.
Year:2008
Editon:1
Publisher:Cambridge University Press
Language:english
File Size:3.4 MB
Format:pdf
ISBNS:9780521055314, 0521055318
Categories: Ebooks

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(Ebook) Algebraic Homotopy 1st Edition by Hans Joachim Baues ISBN 0521055318 9780521055314

(Ebook) Algebraic Homotopy 1st Edition by Hans Joachim Baues - Ebook PDF Instant Download/Delivery: 0521055318, 9780521055314
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ISBN 10: 0521055318 
ISBN 13: 9780521055314
Author: Hans Joachim Baues

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.

(Ebook) Algebraic Homotopy 1st Table of contents:

  1. Preface

  2. Introduction

  3. List of Symbols

  4. Axioms for Homotopy Theory and Examples of Cofibration Categories

  5. Homotopy Theory in a Cofibration Category

  6. The Homotopy Spectral Sequences in a Cofibration Category

  7. Extensions, Coverings and Cohomology Groups of a Category

  8. Maps Between Mapping Cones

  9. Homotopy Theory of CW-Complexes

  10. Homotopy Theory of Complexes in a Cofibration Category

  11. Homotopy Theory of Postnikov Towers and the Sullivan–de Rham Equivalence of Rational Homotopy Categories

  12. Homotopy Theory of Reduced Complexes

  13. Bibliography

  14. Index

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Tags: Hans Joachim Baues, Algebraic, Homotopy

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