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 Title Algebraic Topology
 Author(s) Allen Hatcher
 Publisher: Cambridge University Press; 1 edition (December 3, 2001)
 Paperback 556 pages
 eBook Online, PDF, 3.82 MB
 Language: English
 ISBN10/ASIN: 0521795400
 ISBN13: 9780521795401
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Book Description
In most major universities one of the three or four basic firstyear graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for selfstudy, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: 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 is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, Hspaces and Hopf algebras, the Brown representability theorem, the James reduced product, the DoldThom theorem, and Steenrod squares and powers.
This introductory textbook in algebraic topology is suitable for use in a course or for selfstudy, 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. A unique feature of the book is the inclusion of many optional topics for which elementary expositions are hard to find. Researchers and students alike will welcome this aspect of the book.
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