Selected Works, Volume 3: Algebraic and Differential Topology

Description

Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field. Contents Editor’s Preface • R. V. Gamkrelidze FOUNDATIONS OF ALGEBRAIC TOPOLOGY Preface to the Second Russian Edition Introduction Notat I. Complexes and Their Homology Groups II. Invariance of Homology Groups III. Continuous Mappings and Fixed Points SMOOTH MANIFOLDS AND THEIR APPLICATIONS IN HOMOTOPY THEORY Preface to the Second Russian Edition Introduction I. Smooth Manifolds and Their Smooth Mappings II. Framed Manifolds III. The Hopf Invariant IV. Classification of the Mappings of ( n + 1)- and ( n + 2)-Dimensional Spheres into an n-Dimensional Sphere References