Algebraic Homotopy

By:

Hans-Joachim Baues

Format:

Paperback / softback

Series:

Cambridge Studies in Advanced Mathematics

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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.

Release date Australia

January 21st, 2008

Author

Hans-Joachim Baues

Audience

Professional & Vocational

Pages

488

Series

Cambridge Studies in Advanced Mathematics

Dimensions

151x228x27

ISBN-13

9780521055314

Product ID

2026507

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