In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology.
This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally.
The author emphasizes the geometric aspects of the subject, which helps students gain intuition.
A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find.
Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers.
Researchers will also welcome this aspect of the book.
- Format: Paperback
- Pages: 556 pages
- Publisher: Cambridge University Press
- Publication Date: 03/12/2001
- Category: Geometry
- ISBN: 9780521795401