| Algebraic Homotopy Contributor(s): Baues, Hans Joachim (Author) |
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ISBN: 0521055318 ISBN-13: 9780521055314 Publisher: Cambridge University Press
Binding Type: Paperback - See All Available Formats & Editions Published: January 2008 Click for more in this series: Cambridge Studies in Advanced Mathematics (Paperback) |
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| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Topology - General |
| Dewey: 514.24 |
| Series: Cambridge Studies in Advanced Mathematics (Paperback) |
| Physical Information: 1.09" H x 6" W x 9" L (1.56 lbs) 488 pages |
| Features: Bibliography, Maps |
| Descriptions, Reviews, Etc. |
| Publisher 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. |
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