Topological Library: Part 1: Cobordisms and Their Applications (Series on Knots and Everything) (Series on Knots and Everything)

This is the first of three volumes collecting the original and now classic works in topology written in the 50s 60s. 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 fibre spaces. This is the translation of the Russian edition published in 2005 with one entry (Milnor s lectures on the h-cobordism) omitted. 1. L.S. Pontrjagin. Smooth manifolds and their applications in homotopy theory -- Introduction -- ch. I. Smooth manifolds and their maps -- ch. II. Framed manifolds -- ch. III. The Hopf invariant -- ch. IV. Classification of mappings -- 2. R. Thom. Some "global" properties ofdifferentiable manifolds / translated by V.O. Manturov with M.M. Postnikov's comments. Introduction. ch. I. Properties of differentiable mappings. ch. II. Submanifolds and homology classes ofa manifold. ch. III. On Steenrods problem. ch. IV. Cobordant differentiable manifolds -- 3. S.P. Novikov. Homotopy properties of Thom complexes / translated by V.O. Manturov. Introduction. ch. I. Thom's spaces. ch. II. Inner honology rings. ch. III. Realization of cycles -- 4. Generalized Poincare's conjecture in dimensions greater than four -- 5. On the structure of manifolds -- 6. On the formal group laws of unoriented and complex cobordism theory -- 7. Formal groups and their role in algebraic topology approach / translated by V.O. Manturov -- 8. Formal groups, power systems and Adams operators / translated by M.L. Glasser