×

Algebraic topology – homology and homotopy. Reprint of the 1975 edition. (English) Zbl 1003.55002

Classics in Mathematics. Berlin: Springer. xii, 526 p. (2002).
In the more than twenty five years since its first appearance, the book has met with favorable response, both in its use as a text and as reference. It is a good course which leads the reader systematically to the point at which he can begin to tackle problems in algebraic topology.
First, the author offers an account of classical homotopy theory: properties of homotopy groups, fibrations, CW-complexes, homotopy properties of CW-complexes, then he turns to homology and cohomology theories, treating them axiomatically and then constructing them using spectra. These ideas are illustrated via three main examples of ordinary homology, \(K\)-theory and bordisms. Next, the author takes up the study of products in homology and cohomology and the related questions of orientability and duality.
The remainder of the book is dedicated to characteristic classes, cohomology operations and homology cooperations, the Adams spectral sequence (all of these are developed in the context of generalized homology theories).
This book remains one of the best sources for the material which every young algebraic topologist should know.

MSC:

55-02 Research exposition (monographs, survey articles) pertaining to algebraic topology
57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
01A75 Collected or selected works; reprintings or translations of classics
PDFBibTeX XMLCite