TOPOLOGICAL LIBRARY - PART 3: SPECTRAL SEQUENCES IN TOPOLOGY (Series on Knots and Everything (Hardcover))

TOPOLOGICAL LIBRARY; Contents; Foreword; 1. J.-P. Serre. Singular homology of fiber spaces (Translated by V.P. Golubyatnikov); Introduction; Chapter I. The notion of spectral sequence; 1. Spectral sequence of a differential group with increasing filtration; 2. The case of graded group; 3. Transgression and suspension; 4. Exact sequence; 5. The cohomology spectral sequence; 6. Spectral sequence of universal covering; Chapter II. Singular homology and cohomology of fiber spaces; 1. Singular cubic homology; 2. Fiber spaces. Definitions and simple properties The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.” Pt. 1. Cobordisms And Their Applications -- Pt. 2. Characteristic Classes And Smooth Structures On Manifolds -- Pt. 3. Spectral Sequernces In Topology. Editors, S.p. Novikov, I.a. Taimanov ; Translated By V.o. Manturov. Translattion Of The Russian Edition Published In 2005--vol. 1, P. [4] Of Cover. Includes Bibliographical References And Indexes. Features classical papers on algebraic and differential topology published in the 1950s - 1960s. This title documents methods and constructions from these works.