Algebraic Topology

Allen Hatcher (Cornell University, New York)

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English

Cambridge University Pres
08 April 2002

Mathematics & Sciences; Geometry; Algebraic topology

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.

By: Allen Hatcher (Cornell University New York)
Imprint: Cambridge University Pres
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm, Spine: 32mm
Weight: 968g
ISBN: 9780521795401
ISBN 10: 0521795400
Pages: 556
Publication Date: 08 April 2002
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Algebraic Topology

'... this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society '... clear and concise ... makes the book useful both as a basis for courses and as a reference work.' Monatshefte fur Mathematik '... the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind ... the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH