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 nontrivial. 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 nonspecialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
About HansJoachim Baues
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Author  :  HansJoachim Baues 
Publisher  :  Cambridge University Press 
Data Published  :  16 February 1989 
ISBN  :  0521333768 
EAN  :  9780521333764 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  488 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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