ABSTRACT

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.

part |113 pages

Foundations of Algebraic Topology

chapter Chapter I|39 pages

Complexes and Their Homology Groups

chapter Chapter II|36 pages

Invariance of Homology Groups

chapter Chapter III|29 pages

Continuous Mappings and Fixed Points

part |138 pages

Smooth Manifolds and their Applications in Homotopy Theory

chapter Chapter I|37 pages

Smooth Manifolds and Their Smooth Mappings

chapter Chapter II|27 pages

Framed Manifolds

chapter Chapter III|24 pages

The Hopf Invariant