Differential Forms in Algebraic Topology (Graduate Texts in Mathematics)

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are 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 of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

• Algebraic Topology
• Differential Geometry: Connections, Curvature, and Characteristic Classes (Graduate Texts in Mathematics)
• Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218)
• An Introduction to Manifolds (Universitext)
• Algebraic Geometry (Graduate Texts in Mathematics)
• A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics)
• Introduction to Topological Manifolds (Graduate Texts in Mathematics)
• Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics)
• Morse Theory (Annals of Mathematic Studies AM-51)
• Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)