edited by S P Novikov (Landau Institute for Theoretical Physics, Russia), I A Taimanov (University of Maryland, USA), &
translated by V O Manturov

Table of Contents (164k)
Preface (64k)
Chapter 1: Smooth manifolds and their applications in homotopy theory (531k)

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.

• Smooth Manifolds and Their Applications in Homotopy Theory (L S Pontrjagin)
• Some “Global” Properties of Differentiable Manifolds (R Thom)
• Homotopy Properties of Thom Complexes (S P Novikov)
• Generalized Poincaré's Conjecture in Dimension Greater Than Four (S Smale)
• On the Structure of Manifolds (S Smale)
• On the Formal Group Laws of Unoriented and Complex Cobordism Theory (D Quillen)
• Formal Groups and Their Role in Algebraic Topology Approach (V M Buchstaber, A S Mishchenko & S P Novikov)
• Formal Groups, Power Systems and Adams Operators (V M Buchstaber & S P Novikov)