UID:
almahu_9948234003702882
Format:
1 online resource (xix, 466 pages) :
,
digital, PDF file(s).
ISBN:
9780511662522 (ebook)
Series Statement:
Cambridge studies in advanced mathematics ; 15
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Additional Edition:
Print version: ISBN 9780521333764
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511662522
