Topological Library - Part 3: Spectral Sequences In Topology

by Serguei Petrovich Novikov (Editor), Iskander A Taymanov (Editor), Vladimir Petrovich Golubyatnikov (Translator)

Overview

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.”

Product Details

ISBN-13:	9789814401302
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	09/18/2012
Series:	Series On Knots And Everything , #50
Pages:	592
Product dimensions:	5.90(w) x 9.00(h) x 1.40(d)

Table of Contents

Foreword ix

1 Singular homology of fiber spaces V. P. Golubyatnikov J.-P. Serre 1

2 Homotopy groups and classes of abelian groups V. P. Golubyatnikov J.-P. Serre 105

3 Cohomology modulo 2 of Eilenberg-MacLane complexes V. P. Golubyatnikov J.-P. Serre 153

4 On cohomology of principal fiber bundles and homogeneous spaces of compact Lie groups V. P. Golubyatnikov A. Borel 191

5 Cohomology mod 2 of some homogeneous spaces V. P. Golubyatnikov A. Borel 319

6 The Steenrod algebra and its dual J. Milnor 357

7 On the structure and applications of the Steenrod algebra J. F. Adams 383

8 Vector bundles and homogeneous spaces M. F. Atiyah F. Hirzebruch 423

9 The methods of algebraic topology from viewpoint of cobordism theory S. P. Novikov 455

Index 573