Fundamentals of algebraic topology / Steven H. Weintraub.

Includes bibliographical references and index.

1. The Basics --
2. The Fundamental Group --
3. Generalized Homology Theory --
4. Ordinary Homology Theory --
5. Singular Homology Theory --
6. Manifolds --
7. Homotopy Theory --
8. Homotopy Theory --
A. Elementary Homological Algebra --
B. Bilinear Forms.- C. Categories and Functors --
Bibliography --
Index.

This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.