Topological Library. Volume III. Spectral Sequences in Topology

Author(s): 
Editors: S.P. Novikov & I.A. Taimanov
Publisher: 
World Scientific
Year: 
2012
ISBN: 
9789814401302
Short description: 

This volume belongs to a three-volume edition devoted to reprint classical papers on algebraic and differential topology published in the 1950s-1960s. This is a collection of carefully chosen classical papers who have had a big impact in the development of algebraic topology during the XX century.

MSC main category: 
55 Algebraic topology
Review: 

This volume belongs to a three-volume edition devoted to reprint classical papers on algebraic and differential topology published in the 1950s-1960s. Some of these papers may be difficult to find, and several of them have been translated (by V.P. Golubyatnikov) into English for this volume.

The first volume was dedicated to Cobordism theory, the second one to Smooth structures on manifolds. The present volume is devoted, as the title says, to Spectral sequences in topology. The papers appearing in the volume are the following:

J.P. Serre. Singular homology of fiber spaces, Ann. Math. 1951.

J.P. Serre. Homotopy groups and classes of abelian groups, Ann. Math. 58 (1953) 268-294.

J.P. Serre. Cohomology modulo 2 of Eilenberg-MacLane complexes, Comment. Math. Helv. 27 (1953) 198-232.

A. Borel. On cohomology of principal fiber bundles and homogeneous spaces of compact Lie groups, Ann. Math. 57 (1953) 115-207.

A. Borel, Cohomology mod 2 of some homogeneous spaces, Comment. Math. Helv. 27 (1953) 165-197.

J. Milnor. The Steenrod algebra and its dual, Ann. Math. 67 (1958) 150-171.

J.F. Adams. On the structure and applications of the Steenrond algebra, Comm. Math. Helv. 32 (1958) 180-214.

M.F. Atiyah and F. Hirzebruch. Vector bundles and homogeneous spaces, Proc. Symp. Purre Math. vol. III, AMS (1961) 7-38.

S.P. Novikov. The methods of algebraic topology from viewpoint of cobordism theory, Izv. Akad. Nauk SSSR, Ser. Mat. Tom 31 (1967) No. 4.

This is a collection of carefully chosen classical papers who have had a big impact in the development of algebraic topology during the XX century. The papers that were published in other languages have been translated into English. All the papers are accompanied by useful comments about further developments or related publications.

This is a nice volume that should not be missing in any Mathematics Library.

Reviewer: 
Vicente Muñoz
Affiliation: 
UCM

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