Differential Forms in Algebraic Topology

This book, which grew out of a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. It stresses concreteness and motivation and assumes a working knowledge of only point-set topology and algebra. The material is structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype for cohomology, the machinery of algebraic topology is made easy to assimilate.