Lecture Notes in Algebraic Topology (Graduate Studies in Mathematics, 35) (Hardcover)

~ Paul Kirk James F. Davis (Author) "1.1. Chain complexes associated to a space..." (more)
Key Phrases: acyclic models theorem, framed bordism classes, path space fibration, Stiefel Whitney (more...)

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Product Description

The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the "big picture", teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Product Details

• Hardcover: 367 pages
• Publisher: American Mathematical Society (August 1, 2001)
• Language: English
• ISBN-10: 0821821601
• ISBN-13: 978-0821821602
• Product Dimensions: 10.2 x 7.2 x 1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,188,347 in Books (See Bestsellers in Books)

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Most Helpful Customer Reviews

2 of 3 people found the following review helpful:

4.0 out of 5 stars Godd for the second step., May 13, 2004

By A Customer

This book is nicely written to explain "tools" of algebraic topology in a small number of pages. However, this is by *no* means a book for beginners, as it assumes its readers to have coverd a basic course.
For beginners I would reommend Hatcher "Algebraic Topology" or Bredon "Topology and Geometry" instead.