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OverviewIn recent years, for solving problems of algebraic topology and, in particular, difficult problems of homotopy theory, algebraic structures more complicated than just a topological monoid, an algebra, a coalgebra, etc., have been used more and more often. A convenient language for describing various structures arising naturally on topological spaces and on their cohomology and homotopy groups is the language of operads and algebras over an operad. This language was proposed by J. P. May in the 1970s to describe the structures on various loop spaces. This book presents a detailed study of the concept of an operad in the categories of topological spaces and of chain complexes. The notions of an algebra and a coalgebra over an operad are introduced, and their properties are investigated. The algebraic structure of the singular chain complex of a topological space is explained, and it is shown how the problem of homotopy classification of topological spaces can be solved using this structure. For algebras and coalgebras over operads, standard constructions are defined, particularly the bar and cobar consturctions. Operad methods are applied to computing the homology of iterated loop spaces, investigating the algebraic structure of generalized cohomology theories, describing cohomology of groups and algebras, computing differential in the Adams spectral sequence for the homotopy groups of the spheres, and some other problems. Full Product DetailsAuthor: SmirnovPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 198 Dimensions: Width: 19.00cm , Height: 1.10cm , Length: 25.40cm Weight: 0.673kg ISBN: 9780821821701ISBN 10: 0821821709 Pages: 235 Publication Date: 28 February 2001 Audience: General/trade , College/higher education , Professional and scholarly , General , Undergraduate Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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