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Algebraic Homotopy by Hans-Joachim Baues
Book DescriptionThis 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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Book DetailsISBN: 9780521333764
(228mm x 152mm x 32mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 16-Feb-1989
Country of Publication: United Kingdom
Books By Author Hans-Joachim Baues
Algebraic Homotopy, Paperback (January 2008)
This book gives a general outlook on homotopy theory.
Homotopy Category of Simply Connected 4-Manifolds, Paperback (April 2003)
Homotopy of 4-manifolds for researchers and graduate students.
Homotopy Type and Homology, Hardback (May 1996)
This book represents a new attempt to classify homotopy types of simply connected CW-complexes. It provides methods and examples of explicit homotopy classification and includes applications to the classification of manifolds.
Commutator Calculus and Groups of Homotopy Classes, Paperback (November 1981)» View all books by Hans-Joachim Baues
In this work the author extends results of rational homotopy theory to a subring of the rationale.
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